About
hyperelliptic(.ncag).info collects the classification of hyperelliptic varieties (quotients of complex tori by finite groups acting freely without translations) in dimensions $2$, $3$ and $4$, together with the invariants computable from the tangent representation.
The numerical invariants are computed from the representation theory of the
holonomy group by the OSCAR scripts in
compute/,
using OSCAR. Everything derivable from
$(G,\rho)$ is recomputed and cross-checked against the published classifications.
See the explained pages for the mathematics and the
references for the literature.
Sources
The classification rests on work of Bagnera–De Franchis (dimension 2), Uchida–Yoshihara, Lange and Catanese–Demleitner (dimension 3), and Demleitner and Demleitner–Gleissner (dimension 4). The Albanese morphism and indecomposability follow Belmans–Demleitner–Núñez.
How to cite
@online{hyperelliptic,
author = {Belmans, Pieter},
title = {hyperelliptic.ncag.info --- the classification of hyperelliptic varieties in dimensions 2, 3 and 4},
url = {https://hyperelliptic.ncag.info},
year = {2026},
}
Author
Maintained by Pieter Belmans.