Work

Meromorphic modular differential equations for the elliptic genus of Calabi--Yau varieties

Year: 2026

Type: preprint

Abstract: We study differential equations -- not necessarily monic -- for Jacobi modular forms. As an application, we derive a second-order differential equation for the elliptic genus of a $K3$ surface involving the logarithmic derivative of the modular invariant $j(τ)$, and we explicitly find a third-order equation with a leading coefficient of weight 12 for the elliptic genus of any four-dimensional Calabi--Yau variety. Furthermore, we propose a simple recursive algorithm for investigating second-order differential equations with leading coefficient $E_4(τ)$ or $E_6(τ)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26768

Authors: Adler, Dmitrii, Gritsenko, Valery

Institutions: National Research University Higher School of Economics, St Petersburg University, Université de Lille, Laboratoire Paul Painlevé

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Research University Higher School of Economics

Award: G7564030120

OpenAlex ID: W7223000583

Cites: 1

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Related to: 10