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arXiv · 1506.00968

The integral cohomology of the Hilbert scheme of two points

Burt Totaro
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Abstract

The Hilbert scheme X^{[a]} of points on a complex manifold X is a compactification of the configuration space of a-element subsets of X. The integral cohomology of X^{[a]} is more subtle than the rational cohomology. In this paper, we compute the mod 2 cohomology of X^{[2]} for any complex manifold X, and the integral cohomology of X^{[2]} when X has torsion-free cohomology. The results of this paper are used in Voisin's work on the universal CH_0 group of cubic hypersurfaces, because the crucial point there is to study the 2-torsion in the Chow group.

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Burt Totaro. 2015-06-02. The integral cohomology of the Hilbert scheme of two points. https://arxiv.org/abs/1506.00968

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