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Elliptic genus and modular differential equations
- Source :
- Journal of Geometry and Physics. 181:104662
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- We study modular differential equations for the basic weak Jacobi forms in one abelian variable with applications to the elliptic genus of Calabi--Yau varieties. We show that the elliptic genus of any $CY_3$ satisfies a differential equation of degree one with respect to the heat operator. For a $K3$ surface or any $CY_5$ the degree of the differential equation is $3$. We prove that for a general $CY_4$ its elliptic genus satisfies a modular differential equation of degree $5$. We give examples of differential equations of degree two with respect to the heat operator similar to the Kaneko--Zagier equation for modular forms in one variable. We find modular differential equations of Kaneko--Zagier type of degree $2$ or $3$ for the second, third and fourth powers of the Jacobi theta-series.<br />16 pages
Details
- ISSN :
- 03930440
- Volume :
- 181
- Database :
- OpenAIRE
- Journal :
- Journal of Geometry and Physics
- Accession number :
- edsair.doi.dedup.....baac898ce7b82c3619595116b03d07ff