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arXiv · 2510.26361

The $C_2$-equivariant ordinary cohomology of complex quadrics I: The antisymmetric case

Steven R. Costenoble·Thomas Hudson
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Abstract

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 $\mathbb{P}^3$.

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BibTeXRIS

Steven R. Costenoble, Thomas Hudson. 2025-10-30. The $C_2$-equivariant ordinary cohomology of complex quadrics I: The antisymmetric case. https://arxiv.org/abs/2510.26361

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