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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$\begingroup$ Take a look at this paper ams.org/journals/jams/1996-9-02/S0894-0347-96-00197-X/… $\endgroup$– YangMillsCommented Jul 13, 2012 at 13:44
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$\begingroup$ Are you trying to understand why the Donaldson-Futaki invariant equals the classical Futaki invariant? $\endgroup$– YangMillsCommented Jul 13, 2012 at 14:01
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$\begingroup$ 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. $\endgroup$– yee yaoCommented Jul 14, 2012 at 8:57
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2 Answers
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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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math.jussieu.fris broken, but a snapshot is saved on the Wayback Machine. The article can also be found at doi:10.1215/S0012-7094-83-05024-X (Zbl 0515.58007). $\endgroup$ Commented Apr 30, 2023 at 22:00
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You could try one or all of these (same authors):
Edidin, Dan; Graham, William, Algebraic cycles and completions of equivariant $K$-theory, Duke Math. J. 144, No. 3, 489-524 (2008). Zbl 1148.14007.
Edidin, Dan; Graham, William, Riemann-Roch for equivariant Chow groups, Duke Math. J. 102, No. 3, 567-594 (2000). Zbl 0997.14002.
Edidin, Dan; Graham, William, Equivariant intersection theory, Invent. Math. 131, No. 3, 595-644 (1998). Zbl 0940.14003.
answered Jul 13, 2012 at 8:00