Hyperelliptic varieties: quotients of complex tori by finite groups

There is a new website, hyperelliptic.ncag.info, on the classification of hyperelliptic (or generalized hyperelliptic) varieties in complex dimensions 2, 3 and 4. For now it lives as a subdomain of ncag.info. A hyperelliptic variety is a quotient $X = T/G$ of a complex torus $T$ by a finite group $G$ acting freely and without translations. In dimension 1 these are the elliptic curves, in dimension 2 the seven bielliptic surfaces of Bagnera and De Franchis; the word has nothing to do with hyperelliptic curves. The remarkable thing is that all the numerical invariants (the Hodge diamond, the order of the canonical bundle, the number of moduli, the irregularity, the polyvector fields, the twisted Hodge numbers, the Hochschild cohomology) depend only on the tangent representation $\rho\colon G \to \mathrm{GL}(V)$, and can be read off from its character theory. The website computes them all with OSCAR, for every group in the classifications of Uchida–Yoshihara, Lange and…