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摘要翻译：
M.Brion证明了紧积分Kaehler流形的不可约子簇的矩映象的一个凸性结果。V.Guillemin和R.Sjamar将这一结果推广到仅由Borel子群保留的不可约子群。在另一个方向上，L.O'Shea和R.Sjamaar证明了由反辛对合固定的子流形的矩映象的凸性结果。类似于Guillemin和Sjamar对Brion定理的推广，本文推广了O'Shea和Sjamar的结果，证明了由Borel子群保持的不可约子群的对合不动集的矩映象的凸性定理。
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英文标题：
《A convexity theorem for the real part of a Borel invariant subvariety》
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作者：
Timothy E. Goldberg
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Symplectic Geometry 辛几何
分类描述：Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统，辛流，经典可积系统
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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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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PDF链接：
https://arxiv.org/pdf/0709.3287
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