Abelian varieties associated to Gaussian lattices
Algebraic Geometry
2012-01-23 v2
Abstract
We associate to a unimodular lattice L, endowed with an automorphism of square -1, a principally polarized abelian variety A:= L_R/L. We show that the configuration of i-invariant theta divisors of A follows a pattern very similar to the classical theory of theta characteristics; as a consequence we find that A has a high number of vanishing thetanulls. When L = E_8 we recover the 10 vanishing thetanulls of the abelian fourfold discovered by R. Varley.
Cite
@article{arxiv.1112.2843,
title = {Abelian varieties associated to Gaussian lattices},
author = {Arnaud Beauville},
journal= {arXiv preprint arXiv:1112.2843},
year = {2012}
}
Comments
The results are extended to all unimodular lattices