论文标题
关于梯度图的半半和点和非亚伯凸度的评论
Remarks on Semistable Points and Nonabelian Convexity of Gradient Maps
论文作者
论文摘要
我们研究了一个真正的还原组$ g $对Kahler歧管$ z $的动作，这是对复杂的还原性谎言组的全态动作的限制。如果$ g \ subset u^\ mathbb {c} $是兼容的，则有一个相应的梯度映射$μ__\ Mathfrak {p} {p}：z \ to \ mathfrak {p} $，其中$ \ mathfrak {g Mathfrak {g} = \ mathfrak {k} {k} \ oplus \ mathak \ a partan $ g $。我们的主要结果是与$ z $上的$ g $ Action相关的一组可分配点的开放性和连接性，这是$ g $ g $ - $ g $ invariant紧凑型lagrangian submanifold $ z $的convexity定理，以及对两范式品种的convexity结果。
We study the action of a real reductive group $G$ on a Kahler manifold $Z$ which is the restriction of a holomorphic action of a complex reductive Lie group $U^\mathbb{C}.$ We assume that the action of $U$, a maximal compact connected subgroup of $U^\mathbb{C}$ on $Z$ is Hamiltonian. If $G\subset U^\mathbb{C}$ is compatible, there is a corresponding gradient map $μ_\mathfrak{p}: Z\to \mathfrak{p}$, where $\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{p}$ is a Cartan decomposition of the Lie algebra of $G$. Our main results are the openness and connectedness of the set of semistable points associated with $G$-action on $Z$, a convexity theorem for the $G$-action on a $G$-invariant compact Lagrangian submanifold of $Z$, and a convexity result for two-orbit variety.
