Open Access
June, 2000 Moduli of Sheaves on Surfaces and Action of the Oscillator Algebra
Vladimir Baranovsky
J. Differential Geom. 55(2): 193-227 (June, 2000). DOI: 10.4310/jdg/1090340878


This paper gives a generalization of some results on Hilbert schemes of points on surfaces. Let MG(r,n) (resp. MU(r,n)) be the Gieseker (resp. Uhlenbeck) compactification of the moduli spaces of stable bundles on a smooth projective surface. We show that, for surfaces satisfying some technical condition:

(a) The natural map MG(r,n) → MU(r,n) generalizing the Hilbert-Chow morphism from the Hilbert scheme of n points on S to the n-th symmetric power, is strictly semi-small in the sense of Goresky-MacPherson with respect to some stratification.

(b) Let Pt(X) be the Intersection Homology Poincare polynomial of X. Generalizing the computation due to Gottsche and Sorgel we prove that the ratio ∑n qnPt(MG(r,n))/∑n qnPt(MU(r,n)) is a character of a certain Heisenberg-type algebra.

(c) Generalizing results of Nakajima we show how to obtain the action of the Heisenberg algebra on the cohomology using correspondences.


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Vladimir Baranovsky. "Moduli of Sheaves on Surfaces and Action of the Oscillator Algebra." J. Differential Geom. 55 (2) 193 - 227, June, 2000.


Published: June, 2000
First available in Project Euclid: 20 July 2004

zbMATH: 1033.14028
MathSciNet: MR1847311
Digital Object Identifier: 10.4310/jdg/1090340878

Rights: Copyright © 2000 Lehigh University

Vol.55 • No. 2 • June, 2000
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