New paper: The integral cohomology of the Hilbert scheme of two points

IMG-20140924-00178I’ve posted a new paper on the arXiv. (I haven’t found an apt cat picture, so have just used a photo of Susie the cat, who supervised the writing of the paper closely.)

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.

Photo: Susie the cat in Princeton.

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