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arXiv · 1112.2843

Abelian varieties associated to Gaussian lattices

Arnaud Beauville
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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.

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Arnaud Beauville. 2012-01-20. Abelian varieties associated to Gaussian lattices. https://arxiv.org/abs/1112.2843

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