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Equivariant Chow groups for torus actions

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Abstract

We study Edidin and Graham's equivariant Chow groups in the case of torus actions. Our main results are: (i) a presentation of equivariant Chow groups in terms of invariant cycles, which shows how to recover usual Chow groups from equivariant ones; (ii) a precise form of the localization theorem for torus actions on projective, nonsingular varieties; (iii) a construction of equivariant multiplicities, as functionals on equivariant Chow groups; (iv) a construction of the action of operators of divided differences on theT-equivariant Chow group of any scheme with an action of a reductive group with maximal torusT. We apply these results to intersection theory on varieties with group actions, especially to Schubert calculus and its generalizations. In particular, we obtain a presentation of the Chow ring of any smooth, projective spherical variety.

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  1. Institut Fourier, B. P. 74, 38402, Saint-Martin d'Hères Cedex, France

    M. Brion

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Brion, M. Equivariant Chow groups for torus actions. Transformation Groups 2, 225–267 (1997). https://doi.org/10.1007/BF01234659

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