Spectrum of equivariant cohomology as a fixed point scheme

2022/12/22 by Tamás Hausel, Kamil Rychlewicz · 1 citation
Mathematics · #math.AG #math.AT

paper · pdf · doi:10.46298/epiga.2025.12591

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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• Variations on cohomology rings and zero schemes

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