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Is there any reference for equivariant Riemann-Roch formula: book, paper, notes or something? I want to compute the weight of the action of C^* on the top wedge of cohomology group.

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Take a look at this paper ams.org/journals/jams/1996-9-02/S0894-0347-96-00197-X/… –  YangMills Jul 13 '12 at 13:44
    
Are you trying to understand why the Donaldson-Futaki invariant equals the classical Futaki invariant? –  YangMills Jul 13 '12 at 14:01
    
yeah,I am trying to use it to compute Donaldson-Futaki invariant of some examples such as Mukai-Tian type 3-fold in Arezzo & Vedova's paper. –  yee yao Jul 14 '12 at 8:57

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up vote 4 down vote accepted

You also have some lecture notes on the web page of Michel Brion here.

This paper of N. Berline and M. Vergne is well written (but is more "Lie Group theoretic" than the previous references and it is written in french...).

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You could try one or all of these (same authors):

Dan Edidin and William Graham:

Algebraic cycles and completions of equivariant K-theory here

Riemann-Roch for equivariant Chow groups here

Equivariant intersection theory here

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