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• W2962794105 abstract "For a complex variety with a torus action we propose a new method of computing Chern-Schwartz-MacPherson classes. The method does not apply resolution of singularities. It is based on the Localization Theorem in equivariant cohomology. Equivariant cohomology is a powerful tool for studying complex mani- folds equipped with a torus action. The Localization Theorem of Atiyah and Bott and the resulting formula of Berline-Vergne allow to compute global invariants, for example invariants of singular subsets, in terms of some data attached to the fixed points of the action. We will concentrate on the equi- variant Chern-Schwartz-MacPherson classes. The global class is determined by the local contributions coming from the fixed points. On the other hand, the sum of the local contributions divided by the Euler classes is equal to zero in an appropriate localization of equivariant cohomology. Especially for Grassmannians we obtain interesting formulas with nontrivial relations involving rational functions. We discuss the issue of positivity: the local equivariant Chern class may be presented in various ways, depending on the choice of generating circles of the torus. For some choices we find that the coecients of the presentation are nonnegative. Also the coecients in the Schur basis are nonnegative in many examples, but it turns out that not always." @default.
• W2962794105 created "2019-07-30" @default.
• W2962794105 creator A5037615802 @default.
• W2962794105 date "2012-01-01" @default.
• W2962794105 modified "2023-09-24" @default.
• W2962794105 title "EQUIVARIANT CHERN CLASSES AND LOCALIZATION THEOREM" @default.
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• W2962794105 doi "https://doi.org/10.5427/jsing.2012.5k" @default.
• W2962794105 hasPublicationYear "2012" @default.
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