论文标题
力矩图的琐碎
Trivializations of moment maps
论文作者
论文摘要
我们研究矩图的各种琐碎化。首先是在平滑仿射品种上作用的还原组$ g $的一般框架。我们证明，在$ h $ $ h $的常规位点上，矩图是本地纤维振动，最大的紧凑型亚组为$ g $。该构建依赖于Kirwan，Ness-Mumford和Sjamaar研究的时刻图的KEMPF-内度理论和莫尔斯理论。然后，我们将其与Nakajima和Kronheimer的想法一起应用，以使Nakajima Quiver品种的Hyperkaehler力矩图微不足道。请注意，关于箭量品种的琐碎结果是由Nakajima和Maffei等专家知道和使用的，但我们无法在文献中找到证据。
We study various trivializations of moment maps. First in the general framework of a reductive group $G$ acting on a smooth affine variety. We prove that the moment map is a locally trivial fibration over a regular locus of the center of the Lie algebra of $H$ a maximal compact subgroup of $G$. The construction relies on Kempf-Ness theory and Morse theory of the square norm of the moment map studied by Kirwan, Ness-Mumford and Sjamaar. Then we apply it together with ideas from Nakajima and Kronheimer to trivialize the hyperkaehler moment map for Nakajima quiver varieties. Notice this trivialization result about quiver varieties was known and used by experts such as Nakajima and Maffei but we could not locate a proof in the literature.
