UCLA

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.