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arXiv · 1912.13218

The integral cohomology of the Hilbert scheme of points on a surface

Burt Totaro
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Abstract

We show that if X is a smooth complex projective surface with torsion-free cohomology, then the Hilbert scheme X^[n] has torsion-free cohomology for every natural number n. This extends earlier work by Markman on the case of Poisson surfaces. The proof uses Gholampour-Thomas's reduced obstruction theory for nested Hilbert schemes of surfaces.

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Burt Totaro. 2019-12-31. The integral cohomology of the Hilbert scheme of points on a surface. https://doi.org/10.1017/fms.2020.35

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