Algebraic cuts
Authors:
Dan Edidin and William Graham
Journal:
Proc. Amer. Math. Soc. 126 (1998), 677685
MSC (1991):
Primary 14D25, 14L30
MathSciNet review:
1459118
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Abstract 
References 
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Additional Information
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.
 [BP]
Michel
Brion and Claudio
Procesi, Action d’un tore dans une variété
projective, Operator algebras, unitary representations, enveloping
algebras, and invariant theory (Paris, 1989) Progr. Math., vol. 92,
Birkhäuser Boston, Boston, MA, 1990, pp. 509–539 (French).
MR
1103602 (92m:14061), http://dx.doi.org/10.1007/s101070100288
 [EG]
D. Edidin, W. Graham, Equivariant intersection theory, Inventiones Math., to appear, alggeo 9609018.
 [EG2]
D. Edidin, W. Graham, Localization in equivariant intersection theory and the Bott residue formula, preprint alggeo 9508001.
 [GK]
V. Guillemin, J. Kalkman, A new proof of the JeffreyKirwan localization theorem, preprint (1994).
 [GIT]
D.
Mumford, J.
Fogarty, and F.
Kirwan, Geometric invariant theory, 3rd ed., Ergebnisse der
Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related
Areas (2)], vol. 34, SpringerVerlag, Berlin, 1994. MR 1304906
(95m:14012)
 [L]
Eugene
Lerman, Symplectic cuts, Math. Res. Lett. 2
(1995), no. 3, 247–258. MR 1338784
(96f:58062), http://dx.doi.org/10.4310/MRL.1995.v2.n3.a2
 [BP]
 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), 509539. MR 92m:14061
 [EG]
 D. Edidin, W. Graham, Equivariant intersection theory, Inventiones Math., to appear, alggeo 9609018.
 [EG2]
 D. Edidin, W. Graham, Localization in equivariant intersection theory and the Bott residue formula, preprint alggeo 9508001.
 [GK]
 V. Guillemin, J. Kalkman, A new proof of the JeffreyKirwan localization theorem, preprint (1994).
 [GIT]
 D. Mumford, J. Fogarty, F. Kirwan, Geometric Invariant Theory, 3rd enlarged edition, SpringerVerlag (1994). MR 95m:14012
 [L]
 E. Lerman, Symplectic cuts, Math. Res. Letters, 2 (1995), 247258. MR 96f:58062
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Additional Information
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:
http://dx.doi.org/10.1090/S0002993998044396
PII:
S 00029939(98)044396
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
Article copyright:
© Copyright 1998
American Mathematical Society
