Launching hyperelliptic.ncag.info
This site collects the classification of hyperelliptic varieties in dimensions $2$, $3$ and $4$, together with the invariants that can be computed from the tangent representation of the holonomy group.
Everything numerical is recomputed from representation theory with OSCAR: the Hodge diamond, the order of the canonical bundle, the number of moduli, the irregularity, the polyvector fields, and more. See invariants from representation theory for the formulas, and the explained pages for background.
The dimension-2 and dimension-3 classifications are complete. In dimension $4$ the $79$ holonomy groups are known, and the tangent representations satisfying the necessary conditions are listed; see completeness in dimension 4.