Proceedings of the American Mathematical Society

Author(s): Dan Edidin; William Graham
Journal: Proc. Amer. Math. Soc. 126 (1998), 677-685.
MSC (1991): Primary 14D25, 14L30
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Abstract: In this note we give an algebraic version of a construction called symplectic cutting, which is due to Lerman. Our construction is valid for projective varieties defined over arbitrary fields. Using the equivariant intersection theory developed by the authors, it is a useful tool for studying quotients by torus actions. At the end of the paper, we give an algebraic proof of the Kalkman residue formula and use it to give some formulas for characteristic numbers of quotients.

[B-P]: M. Brion, C. Procesi, Action d'un tore dans une variété projective, in Operator algebras, unitary representations, and invariant theory (Paris 1989), Prog. in Math. 92 (1990), 509-539. MR 92m:14061
[E-G]: D. Edidin, W. Graham, Equivariant intersection theory, Inventiones Math., to appear, alg-geo 9609018.
[E-G2]: D. Edidin, W. Graham, Localization in equivariant intersection theory and the Bott residue formula, preprint alg-geo 9508001.
[G-K]: V. Guillemin, J. Kalkman, A new proof of the Jeffrey-Kirwan localization theorem, preprint (1994).
[GIT]: D. Mumford, J. Fogarty, F. Kirwan, Geometric Invariant Theory, 3rd enlarged edition, Springer-Verlag (1994). MR 95m:14012
[L]: E. Lerman, Symplectic cuts, Math. Res. Letters, 2 (1995), 247-258. MR 96f:58062

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14D25, 14L30

Dan Edidin
Affiliation: Department of Mathematics, University of Missouri, Columbia Missouri 65211
Email: edidin@cantor.math.missouri.edu

William Graham
Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Address at time of publication: Department of Mathematics, University of Georgia, Athens, Georgia 30602

DOI: 10.1090/S0002-9939-98-04439-6
PII: S 0002-9939(98)04439-6
Keywords: Geometric invariant theory, Chow groups
Received by editor(s): September 6, 1996
Additional Notes: The first author was partially supported by the NSF, and the University of Missouri Research Board.
Communicated by: Ron Donagi
Copyright of article: Copyright 1998, American Mathematical Society

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