PreprintarXiv licencearXiv
Meromorphic modular differential equations for the elliptic genus of Calabi--Yau varieties
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 E4(τ) or E6(τ).
Related
- Meromorphic approximation of holomorphic maps into algebraically elliptic projective varieties
- Explicit meromorphic solutions of certain types of nonlinear differential-difference equations
- Meromorphic solutions of first-order differential equations with rational exponential coefficients
- Holonomic sequences arising from meromorphic modular forms
- Hyperbolic Area Methods in Meromorphic Dynamics and Elliptic Polynomial Skew Products
BibTeX
@misc{adler2026meromorphic,
title = {{Meromorphic modular differential equations for the elliptic genus of Calabi--Yau varieties}},
author = {Dmitrii Adler and Valery Gritsenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26768},
eprint = {2610.26768},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26768},
}
RIS
TY - UNPB
TI - Meromorphic modular differential equations for the elliptic genus of Calabi--Yau varieties
AU - Dmitrii Adler
AU - Valery Gritsenko
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26768
UR - https://arxiv.org/abs/2610.26768
AB - 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).
ER -