Abelian varieties associated to Gaussian lattices

Details Abelian varieties associated to Gaussian lattices Abelian varieties associated to Gaussian lattices

2011-12-13

arxiv.org/abs/1112.2843v2

Mathematics

Algebraic Geometry

The results are extended to all unimodular lattices

Scientific paper

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.

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