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arXiv · 1505.06370

Vector-valued modular forms and the Gauss map

Francesco Dalla Piazza·Alessio Fiorentino·Samuel Grushevsky·Sara Perna·Riccardo Salvati Manni
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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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Francesco Dalla Piazza, Alessio Fiorentino, Samuel Grushevsky, Sara Perna, Riccardo Salvati Manni. 2015-05-23. Vector-valued modular forms and the Gauss map. https://arxiv.org/abs/1505.06370

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