Tamás Hausel ; Kamil Rychlewicz - Spectrum of equivariant cohomology as a fixed point scheme

epiga:12591 - Épijournal de Géométrie Algébrique, February 3, 2025, Volume 9 - https://doi.org/10.46298/epiga.2025.12591
Spectrum of equivariant cohomology as a fixed point schemeArticle

Authors: Tamás Hausel ; Kamil Rychlewicz

    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.


    Volume: Volume 9
    Published on: February 3, 2025
    Accepted on: May 8, 2024
    Submitted on: November 24, 2023
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Algebraic Topology,14L30, 55N91

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