Stringy Hodge numbers and Virasoro algebra

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Let X be an arbitrary smooth n-dimensional projective variety. It was discovered by Libgober and Wood that the product of the Chern classes c₁(X)cₙ₋₁(X) depends only on the Hodge numbers of X. This result has been used by Eguchi, Jinzenji and Xiong in their approach to the quantum cohomology of X via a representation of the Virasoro algebra with the central charge cₙ(X). In this paper we define for singular varieties X a rational number cst¹,ⁿ⁻¹(X) which is a stringy version of the number c₁cₙ₋₁ for smooth n-folds. We show that the number cst¹,ⁿ⁻¹(X) can be expressed in the same way using the stringy Hodge numbers of X. Our results provides an evidence for the existence of an approach to quantum cohomology of singular varieties X via a representation of the Virasoro algebra whose central charge is the rational number est(X) which equals the stringy Euler number of X.