Work

Modular differential equations of minimal orders of the elliptic genus of Calabi--Yau varieties

Year: 2025

Type: preprint

Abstract: We study modular differential equations (MDEs) of high orders for weak Jacobi forms and find necessary conditions for weak Jacobi forms to satisfy MDEs of order 3 with respect to the heat operator. We investigate all possible MDEs for the elliptic genus of six-dimensional manifolds with a trivial first Chern class. We prove that the minimal possible order of the MDE for the elliptic genus of a strict six-dimensional Calabi--Yau variety is four, and find MDEs of order 7 for hyperkähler varieties of dimension 6. The latter MDEs correspond to the generic case. The non-generic weak Jacobi forms of weight 0 and index 3 form a divisor that contains two cubic plane curves in the coefficient space.

Source: arXiv (Cornell University)

Authors: Adler, Dmitrii, Gritsenko, Valery

Institutions: National Research University Higher School of Economics, Université de Lille, Max Planck Institute for Mathematics, Laboratoire Paul Painlevé

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Research University Higher School of Economics

OpenAlex ID: W7084448185

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