Vector-Valued Modular Forms and the Gauss Map
Francesco Dalla Piazza
Riccardo Salvati Manni
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.
Cite this article
Francesco Dalla Piazza, Alessio Fiorentino, Samuel Grushevsky, Sara Perna, Riccardo Salvati Manni, Vector-Valued Modular Forms and the Gauss Map. Doc. Math. 22 (2017), pp. 1063–1080DOI 10.4171/DM/587