Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms

Details Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms

1999-06-28

arxiv.org/abs/math/9906190v1

Mathematics

Algebraic Geometry

To appear in Algebra i Analiz (St. Petersburg Math. Journal) 11:5 (1999); AMS-TeX, 25 pages

Scientific paper

In the paper we study two types of relations: a one is between the elliptic genus of Calabi-Yau manifolds and Jacobi modular forms, another one is between the second quantized elliptic genus, Siegel modular forms and Lorentzian Kac-Moody Lie algebras. We also determine the structure of the graded ring of the weak Jacobi forms with integral Fourier coefficients. It gives us a number of applications to the theory of elliptic genus and of the second quantized elliptic genus.

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