Mathematical Research Letters

Volume 7, Issue 2, March 2000 pp. 155-164.

Stringy Hodge numbers and Virasoro algebra

Authors: Victor V. Batyrev
Author institution: Universität Tübingen

Summary: In this paper we define for singular varieties $X$ a rational number $c_{\rm st}^{1,n-1}(X)$ which is a stringy version of the product of Chern numbers $c_1$ and $c_{n-1}$ We show that the number $c_{\rm st}^{1,n-1}(X)$ can be expressed via stringy Hodge numbers of singular $X$ in the same way as $c_1c_{n-1}$ expresses via usual Hodge numbers for smooth manifolds. Our result provides some evidences for the existence of quantum cohomology theory of singular varieties $X$ based on representation of the Virasoro algebra whose central charge is the rational number $e_{\rm st}(X)$ which equals the stringy Euler number of $X$.

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