Vector-valued modular forms and the Gauss map
Algebraic Geometry
2015-12-14 v1
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.
Cite
@article{arxiv.1505.06370,
title = {Vector-valued modular forms and the Gauss map},
author = {Francesco Dalla Piazza and Alessio Fiorentino and Samuel Grushevsky and Sara Perna and Riccardo Salvati Manni},
journal= {arXiv preprint arXiv:1505.06370},
year = {2015}
}