Delocalized Equivariant Cohomology of Symmetric Products
نویسنده
چکیده
For any closed complex manifold X, we calculate the Poincaré and Hodge polynomials of the delocalized equivariant cohomology H(X, Sn) with a grading specified by physicists. As a consequence, we recover a special case of a formula for the elliptic genera of symmetric products in DijkgraafMoore-Verlinde-Verlinde [8]. For a projective surface X, our results matches with the corresponding formulas for the Hilbert scheme of X[n]. We also give geometric construction of an action of a Heisenberg superalgebra on ∑ n≥0 H (X, Sn), imitating the constructions for equivariant K-theory by Segal [25] and Wang [27]. There is a corresponding version for H.
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تاریخ انتشار 1999