Integral cohomology of quotients via toric geometry
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866912291037904896 |
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| author | Menet, Grégoire |
| author_facet | Menet, Grégoire |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_05953 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Integral cohomology of quotients via toric geometry Menet, Grégoire Algebraic Geometry Geometric Topology 14F43, 14M25, 53C26, 55N10 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. |
| title | Integral cohomology of quotients via toric geometry |
| topic | Algebraic Geometry Geometric Topology 14F43, 14M25, 53C26, 55N10 |
| url | https://arxiv.org/abs/1908.05953 |