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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Algebraic cuts
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by Dan Edidin and William Graham PDF
Proc. Amer. Math. Soc. 126 (1998), 677-685 Request permission

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.
References
  • 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, DOI 10.1007/s101070100288
  • D. Edidin, W. Graham, Equivariant intersection theory, Inventiones Math., to appear, alg-geo 9609018.
  • D. Edidin, W. Graham, Localization in equivariant intersection theory and the Bott residue formula, preprint alg-geo 9508001.
  • V. Guillemin, J. Kalkman, A new proof of the Jeffrey-Kirwan localization theorem, preprint (1994).
  • 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, DOI 10.1007/978-3-642-57916-5
  • Eugene Lerman, Symplectic cuts, Math. Res. Lett. 2 (1995), no. 3, 247–258. MR 1338784, DOI 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
  • 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 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 677-685
  • MSC (1991): Primary 14D25, 14L30
  • DOI: https://doi.org/10.1090/S0002-9939-98-04439-6
  • MathSciNet review: 1459118