Algebraic cuts

Authors:
Dan Edidin and William Graham

Journal:
Proc. Amer. Math. Soc. **126** (1998), 677-685

MSC (1991):
Primary 14D25, 14L30

MathSciNet review:
1459118

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Abstract | References | Similar Articles | 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.

**[B-P]**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**, 10.1007/s101070100288**[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, and F. Kirwan,*Geometric invariant theory*, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], vol. 34, Springer-Verlag, Berlin, 1994. MR**1304906****[L]**Eugene Lerman,*Symplectic cuts*, Math. Res. Lett.**2**(1995), no. 3, 247–258. MR**1338784**, 10.4310/MRL.1995.v2.n3.a2

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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:
https://doi.org/10.1090/S0002-9939-98-04439-6

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

Article copyright:
© Copyright 1998
American Mathematical Society