Vector-valued modular forms and the Gauss map (Q1677379)

Summary: 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.