Borel不变子簇的实部的一个凸性定理
A convexity theorem for the real part of a Borel invariant subvariety
摘要：
M. Brion证明了由Hamilton群作用的复化所保持的紧致积分Kaehler流形的不可约子簇的矩映射象的凸性结果。V. Guillemin和R. Sjamaar将这一结果推广到仅由博雷尔子群保持的不可约子簇。在另一个方向，L。O'Shea和R. Sjamaar证明了由反辛对合固定的子流形的矩映射象的凸性结果。类似于Guillemin和Sjamaar对Brion定理的推广，本文推广了O'Shea和Sjamaar的结果，证明了博雷尔子群所保持的不可约子簇的对合不动集的矩映射象的一个凸性定理.
英文摘要：
M. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kaehler 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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