Differentiating Siegel Modular Forms and the Moving Slope of Ag

Samuel Grushevsky; Tomoyoshi Ibukiyama; Gabriele Mondello; Riccardo Salvati Manni

doi:10.1093/imrn/rnad203

Differentiating Siegel Modular Forms and the Moving Slope of A_g

Samuel Grushevsky
, Tomoyoshi Ibukiyama
, Gabriele Mondello
, Riccardo Salvati Manni

Simons Center for Geometry & Physics

The University of Osaka
University of Rome La Sapienza

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

Abstract

We study the cone of moving divisors on the moduli space A_g of principally polarized abelian varieties. Partly motivated by the generalized Rankin–Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel modular forms, and we apply it to produce new modular forms.

Original language	English
Pages (from-to)	3442-3486
Number of pages	45
Journal	International Mathematics Research Notices
Volume	2024
Issue number	4
DOIs	https://doi.org/10.1093/imrn/rnad203
State	Published - Feb 1 2024

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10.1093/imrn/rnad203

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title = "Differentiating Siegel Modular Forms and the Moving Slope of Ag",

abstract = "We study the cone of moving divisors on the moduli space Ag of principally polarized abelian varieties. Partly motivated by the generalized Rankin–Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel modular forms, and we apply it to produce new modular forms.",

author = "Samuel Grushevsky and Tomoyoshi Ibukiyama and Gabriele Mondello and Manni, \{Riccardo Salvati\}",

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AU - Grushevsky, Samuel

AU - Ibukiyama, Tomoyoshi

AU - Mondello, Gabriele

AU - Manni, Riccardo Salvati

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N2 - We study the cone of moving divisors on the moduli space Ag of principally polarized abelian varieties. Partly motivated by the generalized Rankin–Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel modular forms, and we apply it to produce new modular forms.

AB - We study the cone of moving divisors on the moduli space Ag of principally polarized abelian varieties. Partly motivated by the generalized Rankin–Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel modular forms, and we apply it to produce new modular forms.

UR - https://www.scopus.com/pages/publications/85186073786

U2 - 10.1093/imrn/rnad203

DO - 10.1093/imrn/rnad203

M3 - Article

AN - SCOPUS:85186073786

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VL - 2024

SP - 3442

EP - 3486

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 4

ER -

Differentiating Siegel Modular Forms and the Moving Slope of A_g

Abstract

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