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

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.

6 pages

References in corpus (1)

• Degeneracy loci, virtual cycles and nested Hilbert schemes I

Cited by in corpus (1)

• Maximal real varieties from moduli constructions