Grégoire Menet - Integral cohomology of quotients via toric geometry

epiga:5762 - Épijournal de Géométrie Algébrique, February 23, 2022, Volume 6 - https://doi.org/10.46298/epiga.2022.volume6.5762
Integral cohomology of quotients via toric geometry

Authors: Grégoire Menet

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.


Volume: Volume 6
Published on: February 23, 2022
Accepted on: February 23, 2022
Submitted on: September 15, 2019
Keywords: Mathematics - Algebraic Geometry,Mathematics - Geometric Topology,14F43, 14M25, 53C26, 55N10


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