Vector-valued modular forms and the Gauss map

2015/05/23 by Francesco Dalla Piazza, Alessio Fiorentino, Piazza, Francesco Dalla +7
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1505.06370

arxiv created 2015/05/23 · arxiv updated 2015/12/14

Abstract

We use the gradients of theta functions at odd two-torsion points --- thought of as vector-valued modular forms --- to construct holomorphic differential forms on the moduli space of principally polarized abelian varieties, and to characterize the locus of decomposable abelian varieties in terms of the Gauss images of two-torsion points.

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