The $C_2$-equivariant ordinary cohomology of complex quadrics I: The antisymmetric case
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914124247597056 |
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| author | Costenoble, Steven R. Hudson, Thomas |
| author_facet | Costenoble, Steven R. Hudson, Thomas |
| contents | In this, the first of three papers about $C_2$-equivariant complex quadrics, we calculate the equivariant ordinary cohomology of smooth antisymmetric quadrics. One of these quadrics coincides with a $C_2$-equivariant Grassmannian, and we use this calculation to prove an equivariant refinement of the result that there are 27 lines on a cubic surface in $\mathbb{P}^3$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $C_2$-equivariant ordinary cohomology of complex quadrics I: The antisymmetric case Costenoble, Steven R. Hudson, Thomas Algebraic Topology Algebraic Geometry 55N91 (Primary), 14M15, 14N15, 55R40, 55R91, 57R20, 57R85 (Secondary) In this, the first of three papers about $C_2$-equivariant complex quadrics, we calculate the equivariant ordinary cohomology of smooth antisymmetric quadrics. One of these quadrics coincides with a $C_2$-equivariant Grassmannian, and we use this calculation to prove an equivariant refinement of the result that there are 27 lines on a cubic surface in $\mathbb{P}^3$. |
| title | The $C_2$-equivariant ordinary cohomology of complex quadrics I: The antisymmetric case |
| topic | Algebraic Topology Algebraic Geometry 55N91 (Primary), 14M15, 14N15, 55R40, 55R91, 57R20, 57R85 (Secondary) |
| url | https://arxiv.org/abs/2510.26361 |