Moduli of Sheaves on Surfaces and Action of the Oscillator Algebra

نویسنده

  • Vladimir BARANOVSKY
چکیده

Let S be a smooth complex projective surface and Hilbn(S) the Hilbert scheme of all length n zero-dimensional subschemes of S. It is known (cf. [Fo]) that Hilbn(S) is a smooth projective variety of dimension 2n. The structure of the cohomology ring ofHilbn(S) for a fixed n is rather difficult to understand. However, when we consider the direct sum ⊕ n≥0 H ∗(Hilbn(S)) (all cohomology in this paper will be with complex coefficients) the picture becomes more comprehensible. Firstly, for any complex smooth algebraic variety X of dimension d, let Pt(X) be the shifted Poincaré polynomial ∑d i=0 t i−d · dimC H i(X). It was shown by Göttsche [Gö1] that, for any smooth quasi-projective surface S

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تاریخ انتشار 2000