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

Abstract

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.

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

References in corpus (3)

• Algebras, BPS States, and Strings
• Counting Dyons in N=4 String Theory
• The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebras

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• Constraints on 2d CFT partition functions
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
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• The Siegel modular forms of genus 2 with the simplest divisor
• BKM Lie superalgebras from counting twisted CHL dyons
• The Largest Mathieu Group and (Mock) Automorphic Forms
• Complex vector bundles and Jacobi forms
• Unravelling Mathieu Moonshine
• Umbral Moonshine and the Niemeier Lattices
• BKM Lie superalgebras from counting twisted CHL dyons -- II
• Second Quantized Mathieu Moonshine
• On the space of elliptic genera
• A Lecture about classification of Lorentzian Kac-Moody algebras of the rank three
• Computing Riemann-Roch polynomials and classifying hyper-Kähler fourfolds
• Elliptic genus of singular algebraic varieties and quotients
• Reflective modular forms: A Jacobi forms approach