1999/06/28 by Valery Gritsenko, V. Gritsenko, Gritsenko, V. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #hep-th #math.AG #math.AT
paper · pdf · doi:10.48550/arxiv.math/9906191
AMS-TeX, 21 pages
arxiv created 1999/06/28 · arxiv updated 2009/11/30
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).