Spectrum of equivariant cohomology as a fixed point scheme
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916047577153536 |
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| author | Hausel, Tamás Rychlewicz, Kamil |
| author_facet | Hausel, Tamás Rychlewicz, Kamil |
| contents | An action of a complex reductive group $\mathrm G$ on a smooth projective variety $X$ is regular when all regular unipotent elements in $\mathrm G$ act with finitely many fixed points. Then the complex $\mathrm G$-equivariant cohomology ring of $X$ is isomorphic to the coordinate ring of a certain regular fixed point scheme. Examples include partial flag varieties, smooth Schubert varieties and Bott-Samelson varieties. We also show that a more general version of the fixed point scheme allows a generalisation to GKM spaces, such as toric varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11836 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spectrum of equivariant cohomology as a fixed point scheme Hausel, Tamás Rychlewicz, Kamil Algebraic Geometry Algebraic Topology 14L30, 55N91 An action of a complex reductive group $\mathrm G$ on a smooth projective variety $X$ is regular when all regular unipotent elements in $\mathrm G$ act with finitely many fixed points. Then the complex $\mathrm G$-equivariant cohomology ring of $X$ is isomorphic to the coordinate ring of a certain regular fixed point scheme. Examples include partial flag varieties, smooth Schubert varieties and Bott-Samelson varieties. We also show that a more general version of the fixed point scheme allows a generalisation to GKM spaces, such as toric varieties. |
| title | Spectrum of equivariant cohomology as a fixed point scheme |
| topic | Algebraic Geometry Algebraic Topology 14L30, 55N91 |
| url | https://arxiv.org/abs/2212.11836 |