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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A convexity theorem for the real part of a Borel invariant subvariety


Author: Timothy E. Goldberg
Journal: Proc. Amer. Math. Soc. 137 (2009), 1447-1458
MSC (2000): Primary 53D20; Secondary 14L24, 53C55
Published electronically: November 10, 2008
MathSciNet review: 2465671
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Abstract: M. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kähler manifold preserved by the complexification of the Hamiltonian group action. V. Guillemin and R. Sjamaar generalized this result to irreducible subvarieties preserved only by a Borel subgroup. In another direction, L. O'Shea and R. Sjamaar proved a convexity result for the moment map image of the submanifold fixed by an antisymplectic involution. Analogous to Guillemin and Sjamaar's generalization of Brion's theorem, in this paper we generalize O'Shea and Sjamaar's result, proving a convexity theorem for the moment map image of the involution fixed set of an irreducible subvariety preserved by a Borel subgroup.


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Additional Information

Timothy E. Goldberg
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850-4201
Email: goldberg@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09764-5
PII: S 0002-9939(08)09764-5
Received by editor(s): January 15, 2008
Published electronically: November 10, 2008
Additional Notes: The author was partially supported by National Science Foundation Grant DMS–0300172.
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.