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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hamiltonian torus actions on
symplectic orbifolds and toric varieties


Authors: Eugene Lerman and Susan Tolman
Journal: Trans. Amer. Math. Soc. 349 (1997), 4201-4230
MSC (1991): Primary 58F05; Secondary 57S15, 14M25
MathSciNet review: 1401525
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Abstract | References | Similar Articles | Additional Information

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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01821-7
PII: S 0002-9947(97)01821-7
Keywords: Symplectic orbifolds, Hamiltonian torus actions, moment map, toric varieties
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.
Article copyright: © Copyright 1997 American Mathematical Society