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.

arXiv commentFinal version published in EPIGA

References in corpus (5)

• The global moduli theory of symplectic varieties
• On natural deformations of symplectic automorphisms of manifolds of K3^[n] type
• Describing toric varieties and their equivariant cohomology
• Automorphisms of generalised Kummer fourfolds
• Computing Cup-Products in integral cohomology of Hilbert schemes of points on K3 surfaces

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