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

Goldberg, Timothy

doi:10.1090/S0002-9939-08-09764-5

A convexity theorem for the real part of a Borel invariant subvariety
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by Timothy E. Goldberg

Proc. Amer. Math. Soc. 137 (2009), 1447-1458

DOI: https://doi.org/10.1090/S0002-9939-08-09764-5

Published electronically: November 10, 2008

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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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