Transformation Groups

, Volume 2, Issue 3, pp 225–267

Equivariant Chow groups for torus actions

  • M. Brion


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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Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • M. Brion
    • 1
  1. 1.Institut FourierSaint-Martin d'Hères CedexFrance

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