Defines virtual cycles for 3-term complexes via blow-up modifications of the complex and applies them to Hilbert schemes of surfaces to strengthen known results on reduced and virtual cycles.
On the Cobordism Class of the Hilbert Scheme of a Surface
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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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math.AG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Virtual cycles of 3-term complexes and the Hilbert schemes of surfaces
Defines virtual cycles for 3-term complexes via blow-up modifications of the complex and applies them to Hilbert schemes of surfaces to strengthen known results on reduced and virtual cycles.