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On the Cobordism Class of the Hilbert Scheme of a Surface

G. Ellingsrud·L. Göttsche·M. Lehn
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Abstract

Let S be a smooth projective surfaces and S^[n] the Hilbert scheme of zero-dimensional subschemes of S of length n. We proof that the class of S^[n] in the complex cobordism ring depends only on the class of the surface itself. Moreover, we compute the cohomology and holomorphic Euler characterisitcs of certain tautological sheaves on S^[n] and prove results on the general structure of certain integrals over polynomials in Chern classes of tautological sheaves.

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G. Ellingsrud, L. Göttsche, M. Lehn. 1999-04-19. On the Cobordism Class of the Hilbert Scheme of a Surface. https://arxiv.org/abs/math/9904095

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