Complex vector bundles and Jacobi forms

Abstract

The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi--Yau manifold. In physics such a function appears as the partition function of N=2 superconformal field theories. In these notes we define the modified Witten genus or the automorphic correction of elliptic genus. It is an automorphic function in two variables for an arbitrary holomorphic vector bundle over a compact complex manifold. This paper is an exposition of the talks given by the author at Symposium "Automorphic forms and L-functions" at RIMS, Kyoto (January, 27, 1999) and at Arbeitstagung in Bonn (June, 20, 1999).

AMS-TeX, 21 pages

References in corpus (5)

• Counting Dyons in N=4 String Theory
• The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebras
• Geometry of (0,2) Landau-Ginzburg Orbifolds
• Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms
• Ramond Sector Characters and N=2 Landau-Ginzburg Models

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• M-Strings
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• Elliptic Genera of singular varieties, orbifold elliptic genus and chiral deRham complex
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• 24 faces of the Borcherds modular form Phi_{12}
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Powers of Jacobi triple product, Cohen's numbers and the Ramanujan $\Delta$-function
• New supersymmetric index of heterotic compactifications with torsion
• Cubic forms, anomaly cancellation and modularity
• A Lecture about classification of Lorentzian Kac-Moody algebras of the rank three
• Higher elliptic genera