Vector-valued modular forms and the gauss map

Francesco Dalla Piazza; Alessio Fiorentino; Samuel Grushevsky; Sara Perna; Riccardo Salvati Manni

Vector-valued modular forms and the gauss map

Francesco Dalla Piazza
, Alessio Fiorentino
, Samuel Grushevsky
, Sara Perna
, Riccardo Salvati Manni

Simons Center for Geometry & Physics

Stony Brook University

University of Rome La Sapienza

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We use the gradients of theta functions at odd twotorsion 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 twotorsion points.

Original language	English
Pages (from-to)	1063-1080
Number of pages	18
Journal	Documenta Mathematica
Volume	22
Issue number	2017
State	Published - 2017

Cite this

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title = "Vector-valued modular forms and the gauss map",

abstract = "We use the gradients of theta functions at odd twotorsion 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 twotorsion points.",

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AU - Piazza, Francesco Dalla

AU - Fiorentino, Alessio

AU - Grushevsky, Samuel

AU - Perna, Sara

AU - Manni, Riccardo Salvati

PY - 2017

Y1 - 2017

N2 - We use the gradients of theta functions at odd twotorsion 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 twotorsion points.

AB - We use the gradients of theta functions at odd twotorsion 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 twotorsion points.

UR - https://www.scopus.com/pages/publications/85034416067

M3 - Article

SN - 1431-0635

VL - 22

SP - 1063

EP - 1080

JO - Documenta Mathematica

JF - Documenta Mathematica

IS - 2017

ER -

Vector-valued modular forms and the gauss map

Abstract

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