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Abelian varieties associated to Gaussian lattices

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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https://hal.archives-ouvertes.fr/hal-00756773
Contributor : Arnaud Beauville <>
Submitted on : Friday, November 23, 2012 - 4:49:07 PM
Last modification on : Monday, October 12, 2020 - 10:27:29 AM

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  • HAL Id : hal-00756773, version 1
  • ARXIV : 1112.2843

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Arnaud Beauville. Abelian varieties associated to Gaussian lattices. A Celebration of Algebraic Geometry, 18, pp.37-44, 2013, Clay Mathematics Proceedings. ⟨hal-00756773⟩

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