Integral cohomology of quotients via toric geometry

Abstract

We describe the integral cohomology of $X/G$ where $X$ is a compact complex manifold and $G$ a cyclic group of prime order with only isolated fixed points. As a preliminary step, we investigate the integral cohomology of toric blow-ups of quotients of ${\mathbb{C}}^n$. We also provide necessary and sufficient conditions for the spectral sequence of equivariant cohomology of $(X,G)$ to degenerate at the second page. As an application, we compute the Beauville--Bogomolov form of $X/G$ when $X$ is a Hilbert scheme of points on a K3 surface and $G$ a symplectic automorphism group of orders 5 or 7.

Final version published in EPIGA

References in corpus (1)

• The global moduli theory of symplectic varieties

Cited by in corpus (2)

• On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four
• The second integral cohomology of moduli spaces of sheaves on K3 and Abelian surfaces