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arXiv · 2212.11836

Spectrum of equivariant cohomology as a fixed point scheme

Tamás Hausel·Kamil Rychlewicz
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Abstract

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.

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Tamás Hausel, Kamil Rychlewicz. 2022-12-22. Spectrum of equivariant cohomology as a fixed point scheme. https://doi.org/10.46298/epiga.2025.12591

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