hyperelliptic(.ncag).info

the classification of hyperelliptic varieties in dimensions 2, 3 and 4

Hyperelliptic fourfolds

In dimension $4$ there are exactly $79$ hyperelliptic groups (Demleitner). For each we list the tangent representations satisfying the necessary conditions (faithful, every element with eigenvalue $1$, $\rho\oplus\bar\rho$ integral) and the invariants they determine; the tangent action itself is shown on each representation's page.

This list contains every hyperelliptic fourfold, but it may contain representations that are not realized: the conditions above are necessary, and sufficiency is established only in special cases (such as the 16 rigid fourfolds). See completeness in dimension 4.
groupvariety$\#G$$q$$\mathrm{h}^{2,0}$$\mathrm{h}^{3,0}$$\mathrm{h}^{4,0}$$\operatorname{ord} \omega_X$moduli$\mathbf{D}^{\mathrm{b}}(X)$
$\mathrm{C}_{2}$no. 123310210indec.
$\mathrm{C}_{2}$no. 22222118indec.
$\mathrm{C}_{2}$no. 321330210indec.
$\mathrm{C}_{3}$no. 13331039indec.
$\mathrm{C}_{3}$no. 23210034indec.
$\mathrm{C}_{3}$no. 33222116indec.
$\mathrm{C}_{3}$no. 43101111indec.
$\mathrm{C}_{3}$no. 53122035indec.
$\mathrm{C}_{4}$no. 14331049indec.
$\mathrm{C}_{4}$no. 24210024indec.
$\mathrm{C}_{4}$no. 34210045indec.
$\mathrm{C}_{4}$no. 44222116indec.
$\mathrm{C}_{4}$no. 54100041indec.
$\mathrm{C}_{4}$no. 64101112indec.
$\mathrm{C}_{4}$no. 74122045indec.
$\mathrm{C}_{4}$no. 84111045indec.
$\mathrm{C}_{4}$no. 94111024indec.
$\mathrm{C}_{5}$no. 15210054indec.
$\mathrm{C}_{2} \times \mathrm{C}_{2}$no. 14210026indec.
$\mathrm{C}_{2} \times \mathrm{C}_{2}$no. 24111026open
$\mathrm{C}_{2} \times \mathrm{C}_{2}$no. 34101114open
$\mathrm{C}_{2} \times \mathrm{C}_{2}$no. 44012026open
$\mathrm{S}_3$no. 16210025indec.
$\mathrm{S}_3$no. 26101113open
$\mathrm{S}_3$no. 36012025open
$\mathrm{C}_{6}$no. 16331069indec.
$\mathrm{C}_{6}$no. 26210065indec.
$\mathrm{C}_{6}$no. 36210035indec.
$\mathrm{C}_{6}$no. 46210064indec.
$\mathrm{C}_{6}$no. 56210024indec.
$\mathrm{C}_{6}$no. 66210034indec.
$\mathrm{C}_{6}$no. 76222116indec.
$\mathrm{C}_{6}$no. 86111035indec.
$\mathrm{C}_{6}$no. 96111065indec.
$\mathrm{C}_{6}$no. 106100062indec.
$\mathrm{C}_{6}$no. 116100032indec.
$\mathrm{C}_{6}$no. 126111024indec.
$\mathrm{C}_{6}$no. 136101112indec.
$\mathrm{C}_{6}$no. 146100062indec.
$\mathrm{C}_{6}$no. 156111024indec.
$\mathrm{C}_{6}$no. 166100021indec.
$\mathrm{C}_{6}$no. 176100061indec.
$\mathrm{C}_{6}$no. 186101111indec.
$\mathrm{C}_{6}$no. 196111063indec.
$\mathrm{C}_{6}$no. 206111033indec.
$\mathrm{C}_{6}$no. 216100031indec.
$\mathrm{C}_{6}$no. 226100021indec.
$\mathrm{C}_{6}$no. 236122065indec.
$\mathrm{C}_{7}$no. 17100071indec.
$\mathrm{C}_{7}$no. 27101111indec.
$\mathrm{C}_{8}$no. 18210024indec.
$\mathrm{C}_{8}$no. 28210044indec.
$\mathrm{C}_{8}$no. 38100041indec.
$\mathrm{C}_{8}$no. 48101111indec.
$\mathrm{C}_{8}$no. 58101112indec.
$\mathrm{C}_{8}$no. 68100042indec.
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 18210045indec.
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 28210024indec.
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 38111045open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 48100022open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 58100022open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 68100043open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 78100043open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 88111024open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 98101112open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 108100041open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 118100022open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 128001022open
$\mathrm{C}_{4} \times \mathrm{C}_{2}$no. 138001043open
$\mathrm{D}_4$no. 18210025indec.
$\mathrm{D}_4$no. 28100023open
$\mathrm{D}_4$no. 38101113open
$\mathrm{D}_4$no. 48001023open
$\mathrm{D}_4$no. 58012025open
$\mathrm{Q}_8$no. 18222115indec.
$\mathrm{Q}_8$no. 28111023open
$\mathrm{C}_{2} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 18100024open
$\mathrm{C}_{2} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 28001024open
$\mathrm{C}_{9}$no. 19100091indec.
$\mathrm{C}_{9}$no. 29100031indec.
$\mathrm{C}_{3} \times \mathrm{C}_{3}$no. 19210034indec.
$\mathrm{C}_{3} \times \mathrm{C}_{3}$no. 29100031open
$\mathrm{C}_{3} \times \mathrm{C}_{3}$no. 39111033open
$\mathrm{C}_{3} \times \mathrm{C}_{3}$no. 49100031open
$\mathrm{C}_{3} \times \mathrm{C}_{3}$no. 59101111open
$\mathrm{C}_{3} \times \mathrm{C}_{3}$no. 69001030open
$\mathrm{C}_{10}$no. 110210054indec.
$\mathrm{C}_{10}$no. 2101000102indec.
$\mathrm{C}_{10}$no. 3101000102indec.
$\mathrm{G}(3,4,2)$no. 112222115indec.
$\mathrm{G}(3,4,2)$no. 212100042open
$\mathrm{G}(3,4,2)$no. 312111042open
$\mathrm{G}(3,4,2)$no. 412111023open
$\mathrm{G}(3,4,2)$no. 512001042open
$\mathrm{C}_{12}$no. 1122100124indec.
$\mathrm{C}_{12}$no. 2122100124indec.
$\mathrm{C}_{12}$no. 312210024indec.
$\mathrm{C}_{12}$no. 412210034indec.
$\mathrm{C}_{12}$no. 5121000121indec.
$\mathrm{C}_{12}$no. 612111043indec.
$\mathrm{C}_{12}$no. 712100061indec.
$\mathrm{C}_{12}$no. 8121000122indec.
$\mathrm{C}_{12}$no. 9121000121indec.
$\mathrm{C}_{12}$no. 1012100041indec.
$\mathrm{C}_{12}$no. 1112111033indec.
$\mathrm{C}_{12}$no. 1212100061indec.
$\mathrm{C}_{12}$no. 1312101111indec.
$\mathrm{C}_{12}$no. 1412100031indec.
$\mathrm{C}_{12}$no. 1512100031indec.
$\mathrm{C}_{12}$no. 1612100041indec.
$\mathrm{C}_{12}$no. 17121000121indec.
$\mathrm{C}_{12}$no. 18121000122indec.
$\mathrm{C}_{12}$no. 19121000121indec.
$\mathrm{C}_{12}$no. 2012111043indec.
$\mathrm{C}_{12}$no. 2112111063indec.
$\mathrm{C}_{12}$no. 2212100041indec.
$\mathrm{C}_{12}$no. 2312101112indec.
$\mathrm{C}_{12}$no. 2412100031indec.
$\mathrm{C}_{12}$no. 2512100062indec.
$\mathrm{C}_{12}$no. 2612100021indec.
$\mathrm{C}_{12}$no. 2712100061indec.
$\mathrm{A}_4$no. 112101112open
$\mathrm{A}_4$no. 212001031open
$\mathrm{S}_3 \times \mathrm{C}_2$no. 112210025indec.
$\mathrm{S}_3 \times \mathrm{C}_2$no. 212101113open
$\mathrm{S}_3 \times \mathrm{C}_2$no. 312100023open
$\mathrm{S}_3 \times \mathrm{C}_2$no. 412100023open
$\mathrm{S}_3 \times \mathrm{C}_2$no. 512012025open
$\mathrm{S}_3 \times \mathrm{C}_2$no. 612001023open
$\mathrm{S}_3 \times \mathrm{C}_2$no. 712001023open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 112210065indec.
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 212210064indec.
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 312210024indec.
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 412111065open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 512100063open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 612100063open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 712100033open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 812100062open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 912100022open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1012100062open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1112100022open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1212100062open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1312100032open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1412111024open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1512101112open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1612100021open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1712100061open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1812100061open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 1912100021open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 2012100061open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 2112101111open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 2212111063open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 2312100031open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 2412001033open
$\mathrm{C}_{6} \times \mathrm{C}_{2}$no. 2512001063open
$\mathrm{C}_{14}$no. 1141000141indec.
$\mathrm{C}_{14}$no. 214100021indec.
$\mathrm{C}_{15}$no. 1151000151indec.
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 116210044indec.
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 216100041open
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 316100042open
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 416111043open
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 516100021open
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 616100041open
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 716100042open
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 816100041open
$\mathrm{C}_{4} \times \mathrm{C}_{4}$no. 916101111open
$(\mathrm{C}_4 \times \mathrm{C}_2) \rtimes \mathrm{C}_2$no. 116100042open
$(\mathrm{C}_4 \times \mathrm{C}_2) \rtimes \mathrm{C}_2$no. 216001042open
$\mathrm{G}(4,4,3)$no. 116100042open
$\mathrm{G}(4,4,3)$no. 216001042open
$\mathrm{C}_{8} \times \mathrm{C}_{2}$no. 116100022open
$\mathrm{C}_{8} \times \mathrm{C}_{2}$no. 216100042open
$\mathrm{C}_{8} \times \mathrm{C}_{2}$no. 316100041open
$\mathrm{C}_{8} \times \mathrm{C}_{2}$no. 416100021open
$\mathrm{G}(8,2,5)$no. 116210044indec.
$\mathrm{G}(8,2,5)$no. 216100042open
$\mathrm{G}(8,2,5)$no. 316100021open
$\mathrm{G}(8,2,5)$no. 416101111open
$\mathrm{G}(8,2,5)$no. 516100042open
$\mathrm{G}(8,2,3)$no. 116210024indec.
$\mathrm{G}(8,2,3)$no. 216100022open
$\mathrm{G}(8,2,3)$no. 316101112open
$\mathrm{G}(8,2,3)$no. 416100022open
$\mathrm{G}(8,2,3)$no. 516001022open
$\mathrm{C}_{4} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 116100043open
$\mathrm{C}_{4} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 216100022open
$\mathrm{C}_{4} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 316100041open
$\mathrm{C}_{4} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 416001043open
$\mathrm{C}_{2} \times \mathrm{D}_4$no. 116100023open
$\mathrm{C}_{2} \times \mathrm{D}_4$no. 216001023open
$\mathrm{D}_4 \circ \mathrm{C}_4$no. 116210024indec.
$\mathrm{D}_4 \circ \mathrm{C}_4$no. 216100022open
$\mathrm{D}_4 \circ \mathrm{C}_4$no. 316100022open
$\mathrm{D}_4 \circ \mathrm{C}_4$no. 416101112open
$\mathrm{D}_4 \circ \mathrm{C}_4$no. 516001022open
$\mathrm{C}_{18}$no. 1181000181indec.
$\mathrm{C}_{18}$no. 218100061indec.
$\mathrm{S}_3 \times \mathrm{C}_3$no. 118210064indec.
$\mathrm{S}_3 \times \mathrm{C}_3$no. 218100032open
$\mathrm{S}_3 \times \mathrm{C}_3$no. 318100062open
$\mathrm{S}_3 \times \mathrm{C}_3$no. 418100061open
$\mathrm{S}_3 \times \mathrm{C}_3$no. 518100021open
$\mathrm{S}_3 \times \mathrm{C}_3$no. 618100032open
$\mathrm{S}_3 \times \mathrm{C}_3$no. 718100031open
$\mathrm{S}_3 \times \mathrm{C}_3$no. 818101111open
$\mathrm{S}_3 \times \mathrm{C}_3$no. 918001032open
$\mathrm{S}_3 \times \mathrm{C}_3$no. 1018001062open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 118210064indec.
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 218210034indec.
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 318100062open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 418100032open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 518100062open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 618100061open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 718100061open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 818100031open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 918111063open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1018100061open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1118100031open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1218100061open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1318100061open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1418100021open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1518100031open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1618100031open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1718111033open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1818100031open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1918101111open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 2018100061open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 2118111063open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 2218100061open
$\mathrm{C}_{6} \times \mathrm{C}_{3}$no. 2318100021open
$\mathrm{C}_{20}$no. 1201000201indec.
$\mathrm{C}_{20}$no. 2201000201indec.
$\mathrm{C}_{10} \times \mathrm{C}_{2}$no. 1201000102open
$\mathrm{G}(3,8,2)$no. 124210044indec.
$\mathrm{G}(3,8,2)$no. 224100021open
$\mathrm{G}(3,8,2)$no. 324100042open
$\mathrm{C}_{24}$no. 124100061indec.
$\mathrm{C}_{24}$no. 2241000121indec.
$\mathrm{C}_{24}$no. 324100031indec.
$\mathrm{C}_{24}$no. 4241000121indec.
$\mathrm{S}_3 \times \mathrm{C}_4$no. 124210024indec.
$\mathrm{S}_3 \times \mathrm{C}_4$no. 224101112open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 324100042open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 424100042open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 524100041open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 624100041open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 724100022open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 824100022open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 924001022open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 1024001042open
$\mathrm{S}_3 \times \mathrm{C}_4$no. 1124001042open
$(\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2$no. 124210024indec.
$(\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2$no. 224100022open
$(\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2$no. 324100022open
$(\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2$no. 424101112open
$(\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2$no. 524001022open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 1242100124indec.
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 2241000122open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 3241000122open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 4241000122open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 5241000122open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 624100022open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 724100062open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 8241000121open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 924100041open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 1024100061open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 11241000121open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 1224111043open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 1324100061open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 1424100061open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 15241000122open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 16241000121open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 17241000121open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 1824100041open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 1924100041open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 2024111063open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 2124100031open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 2224100061open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 2324100021open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 2424100061open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 2524100061open
$\mathrm{C}_{12} \times \mathrm{C}_{2}$no. 2624100041open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 124210064indec.
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 224100062open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 324100032open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 424100062open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 524100061open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 624100021open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 724100062open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 824100061open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 924100021open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 1024100032open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 1124100031open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 1224101111open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 1324001032open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 1424001062open
$\mathrm{C}_{3} \times \mathrm{D}_4$no. 1524001062open
$\mathrm{C}_{3} \times \mathrm{Q}_8$no. 124210034indec.
$\mathrm{C}_{3} \times \mathrm{Q}_8$no. 224100062open
$\mathrm{C}_{3} \times \mathrm{Q}_8$no. 324111032open
$\mathrm{C}_{3} \times \mathrm{Q}_8$no. 424100031open
$\mathrm{C}_{3} \times \mathrm{Q}_8$no. 524101111open
$\mathrm{C}_{3} \times \mathrm{Q}_8$no. 624111062open
$\mathrm{C}_{3} \times \mathrm{Q}_8$no. 724100061open
$\mathrm{C}_{3} \times \mathrm{Q}_8$no. 824100021open
$\mathrm{C}_{2} \times \mathrm{A}_4$no. 124100022open
$\mathrm{C}_{2} \times \mathrm{A}_4$no. 224001022open
$\mathrm{C}_{2} \times \mathrm{A}_4$no. 324001061open
$\mathrm{C}_{6} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 124100063open
$\mathrm{C}_{6} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 224100062open
$\mathrm{C}_{6} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 324100022open
$\mathrm{C}_{6} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 424100021open
$\mathrm{C}_{6} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 524100061open
$\mathrm{C}_{6} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 624001063open
$\mathrm{Heis}(3)$no. 127101111open
$\mathrm{Heis}(3)$no. 227001030open
$\mathrm{C}_{3} \times \mathrm{C}_{3} \times \mathrm{C}_{3}$no. 127100031open
$\mathrm{C}_{30}$no. 1301000151indec.
$\mathrm{C}_{30}$no. 2301000301indec.
$\mathrm{C}_{30}$no. 3301000301indec.
$\mathrm{C}_{8} \times \mathrm{C}_{4}$no. 132100041open
$\mathrm{C}_{8} \times \mathrm{C}_{4}$no. 232100041open
$\mathrm{G}(8,4,5)$no. 132100041open
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 132210044indec.
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 232100042open
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 332100021open
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 432100021open
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 532101111open
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 632100021open
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 732100042open
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 832100042open
$\mathrm{C}_{4} \times \mathrm{C}_{4} \times \mathrm{C}_{2}$no. 132100042open
$\mathrm{C}_{4} \times \mathrm{C}_{4} \times \mathrm{C}_{2}$no. 232100041open
$\mathrm{C}_{4} \times \mathrm{C}_{4} \times \mathrm{C}_{2}$no. 332100021open
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$no. 132100041open
$\mathrm{G}(8,4,5) \times \mathrm{C}_2$no. 132100042open
$\mathrm{G}(8,4,5) \times \mathrm{C}_2$no. 232100021open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 136210034indec.
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 236111032open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 336100031open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 436101111open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 5361000121open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 6361000121open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 736100062open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 836111062open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 936100061open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$no. 1036100021open
$\mathrm{C}_{12} \times \mathrm{C}_{3}$no. 1361000121open
$\mathrm{C}_{12} \times \mathrm{C}_{3}$no. 2361000121open
$\mathrm{C}_{12} \times \mathrm{C}_{3}$no. 336100061open
$\mathrm{C}_{12} \times \mathrm{C}_{3}$no. 436100031open
$\mathrm{C}_{12} \times \mathrm{C}_{3}$no. 5361000121open
$\mathrm{C}_{12} \times \mathrm{C}_{3}$no. 636100031open
$\mathrm{C}_{12} \times \mathrm{C}_{3}$no. 736100061open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 136210064indec.
$\mathrm{S}_3 \times \mathrm{C}_6$no. 236100062open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 336100062open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 436100032open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 536100062open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 636100061open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 736100021open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 836100062open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 936100062open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1036100061open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1136100061open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1236100021open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1336100021open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1436100032open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1536100031open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1636101111open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1736001032open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1836001062open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 1936001062open
$\mathrm{S}_3 \times \mathrm{C}_6$no. 2036001062open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 136210064indec.
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 236100062open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 336100062open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 436100062open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 536100032open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 636100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 736100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 836100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 936100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1036100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1136100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1236100021open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1336100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1436100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1536100031open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1636111063open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1736100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1836100031open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 1936100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 2036100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 2136100021open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 2236100031open
$\mathrm{C}_{6} \times \mathrm{C}_{6}$no. 2336101111open
$\mathrm{C}_{20} \times \mathrm{C}_{2}$no. 1401000201open
$\mathrm{C}_{12} \times \mathrm{C}_{4}$no. 1481000121open
$\mathrm{C}_{12} \times \mathrm{C}_{4}$no. 2481000121open
$\mathrm{C}_{12} \times \mathrm{C}_{4}$no. 3481000121open
$\mathrm{C}_{12} \times \mathrm{C}_{4}$no. 448100041open
$\mathrm{C}_{12} \times \mathrm{C}_{4}$no. 5481000121open
$((\mathrm{C}_4 \times \mathrm{C}_2) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 1481000121open
$\mathrm{G}(4,4,3) \times \mathrm{C}_3$no. 1481000121open
$\mathrm{C}_{24} \times \mathrm{C}_{2}$no. 148100061open
$\mathrm{C}_{24} \times \mathrm{C}_{2}$no. 2481000121open
$\mathrm{C}_{4} \times \mathrm{A}_4$no. 148100041open
$\mathrm{C}_{4} \times \mathrm{A}_4$no. 248001041open
$\mathrm{C}_{12} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 1481000122open
$\mathrm{C}_{12} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 2481000121open
$\mathrm{C}_{12} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 348100041open
$\mathrm{C}_{12} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$no. 448100061open
$\mathrm{S}_3 \times \mathrm{C}_3 \times \mathrm{C}_3$no. 154100061open
$\mathrm{S}_3 \times \mathrm{C}_3 \times \mathrm{C}_3$no. 254100031open
$\mathrm{C}_{6} \times \mathrm{C}_{3} \times \mathrm{C}_{3}$no. 154100061open
$\mathrm{C}_{6} \times \mathrm{C}_{3} \times \mathrm{C}_{3}$no. 254100031open
$\mathrm{C}_{6} \times \mathrm{C}_{3} \times \mathrm{C}_{3}$no. 354100061open
$\mathrm{C}_{30} \times \mathrm{C}_{2}$no. 1601000301open
$\mathrm{G}(3,8,2) \times \mathrm{C}_3$no. 1721000121open
$\mathrm{G}(3,8,2) \times \mathrm{C}_3$no. 2721000121open
$\mathrm{S}_3 \times \mathrm{C}_{12}$no. 172100061open
$\mathrm{S}_3 \times \mathrm{C}_{12}$no. 272100061open
$\mathrm{S}_3 \times \mathrm{C}_{12}$no. 3721000121open
$\mathrm{S}_3 \times \mathrm{C}_{12}$no. 4721000121open
$\mathrm{S}_3 \times \mathrm{C}_{12}$no. 572100061open
$\mathrm{S}_3 \times \mathrm{C}_{12}$no. 672100031open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 172210064indec.
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 272100062open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 372100062open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 472100032open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 572100061open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 672100061open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 772100021open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 872100061open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 972100061open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 1072100021open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 1172100061open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 1272100061open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 1372100021open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 1472100031open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 1572100031open
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$no. 1672101111open
$\mathrm{C}_{12} \times \mathrm{C}_{6}$no. 1721000121open
$\mathrm{C}_{12} \times \mathrm{C}_{6}$no. 2721000121open
$\mathrm{C}_{12} \times \mathrm{C}_{6}$no. 3721000121open
$\mathrm{C}_{12} \times \mathrm{C}_{6}$no. 4721000121open
$\mathrm{C}_{12} \times \mathrm{C}_{6}$no. 572100061open
$\mathrm{C}_{12} \times \mathrm{C}_{6}$no. 672100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$no. 172100062open
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$no. 272100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$no. 372100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$no. 472100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$no. 572100021open
$\mathrm{C}_{12} \times \mathrm{C}_{4} \times \mathrm{C}_{2}$no. 1961000121open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3 \times \mathrm{C}_3$no. 1108100031open
$\mathrm{G}(3,4,2) \times \mathrm{C}_3 \times \mathrm{C}_3$no. 2108100061open
$\mathrm{S}_3 \times \mathrm{C}_6 \times \mathrm{C}_3$no. 1108100061open
$\mathrm{S}_3 \times \mathrm{C}_6 \times \mathrm{C}_3$no. 2108100061open
$\mathrm{S}_3 \times \mathrm{C}_6 \times \mathrm{C}_3$no. 3108100061open
$\mathrm{S}_3 \times \mathrm{C}_6 \times \mathrm{C}_3$no. 4108100031open
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{3}$no. 1108100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{3}$no. 2108100061open
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{3}$no. 3108100031open
$\mathrm{C}_{12} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$no. 11441000121open

References

  1. A. Demleitner, The classification of hyperelliptic groups in dimension 4. arXiv:2211.07998
  2. A. Demleitner, C. Gleissner, The classification of rigid hyperelliptic fourfolds, Ann. Mat. Pura Appl. (4) 202 (2023) 1425–1450. MR4576947 doi