Abelian varieties associated to Gaussian lattices

Arnaud Beauville (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Géométrie algébrique [math.AG]

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