JournalsdmVol. 22pp. 1063–1080

Vector-Valued Modular Forms and the Gauss Map

  • Francesco Dalla Piazza

    Sapienza University of Rome, Italy

  • Alessio Fiorentino

    Sapienza University of Rome, Italy

  • Samuel Grushevsky

    Stony Brook University, United States of America

  • Sara Perna

    Sapienza University of Rome, Italy

  • Riccardo Salvati Manni

    Sapienza University of Rome, Italy
Vector-Valued Modular Forms and the Gauss Map cover
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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.

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. 1063–1080

DOI 10.4171/DM/587