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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Hamiltonian torus actions on symplectic orbifolds and toric varieties
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by Eugene Lerman and Susan Tolman PDF
Trans. Amer. Math. Soc. 349 (1997), 4201-4230 Request permission

Abstract:

In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly, we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half, we prove that compact symplectic orbifolds with completely integrable torus actions are classified by convex simple rational polytopes with a positive integer attached to each open facet and that all such orbifolds are algebraic toric varieties.
References
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Additional Information
  • Eugene Lerman
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Address at time of publication: Department of Mathematics, Unversity of Illinois at Urbana-Champaign, 1409 West Green St., Urbana, Illinois 61801
  • Email: lerman@math.uiuc.edu
  • Susan Tolman
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; Current address $\mathrm {(both authors)}$: $\mathrm {Department of Mathematics, University of Illinois at Urbana}$ -$\mathrm {Champaign, 1409 West Green St., Urbana, Illinois 61801}$
  • Address at time of publication: Department of Mathematics, Unversity of Illinois at Urbana-Champaign, 1409 West Green St., Urbana, Illinois 61801
  • Email: tolman@math.princeton.edu
  • Received by editor(s): July 27, 1995
  • Received by editor(s) in revised form: April 22, 1996
  • Additional Notes: Both authors were partially supported by NSF postdoctoral fellowships.
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 4201-4230
  • MSC (1991): Primary 58F05; Secondary 57S15, 14M25
  • DOI: https://doi.org/10.1090/S0002-9947-97-01821-7
  • MathSciNet review: 1401525