THE INTEGRAL COHOMOLOGY OF THE HILBERT SCHEME OF TWO POINTS

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.

Keywords

• 14C05 (primary)
• 55R80 (secondary)