论文标题
feix-kaledin公制在cotangent束的总空间上
Feix-Kaledin metric on the total spaces of cotangent bundles to Kähler quotients
论文作者
论文摘要
在本文中，我们研究了一个cotangent捆绑包的总空间$ y $的几何形状到kähler歧管$ n $，其中$ n $是从$ \ mathbb c^n $减少的。使用Hyperkähler减少，我们在$ y $上构建了HyperKähler指标，并证明它与规范的Feix-Kaledin公制相吻合。该指标通常是不完整的。我们表明，$ y $的度量完成$ \ tilde y $配备了分层Hyperkähler空间的结构。我们为Feix-kaledin指标提供了必要的条件，可以使用R.Bielawski的观察到完成。从$ \ tilde y $上选择一个复杂的结构$ j $。假设$ j \ ne \ pm i $其中$ i $是复杂的结构，其限制$ y = t^*n $是由$ n $上的复杂结构引起的。我们证明了空间$ \ tilde {y} _j $接受代数结构，并且是仿射品种。
In this paper we study the geometry of the total space $Y$ of a cotangent bundle to a Kähler manifold $N$ where $N$ is obtained as a Kähler reduction from $\mathbb C^n$. Using the hyperkähler reduction we construct a hyperkähler metric on $Y$ and prove that it coincides with the canonical Feix-Kaledin metric. This metric is in general non-complete. We show that the metric completion $\tilde Y$ of the space $Y$ is equipped with a structure of a stratified hyperkähler space. We give a necessary condition for the Feix-Kaledin metric to be complete using an observation of R.Bielawski. Pick a complex structure $J$ on $\tilde Y$ induced from quaternions. Suppose that $J\ne\pm I$ where $I$ is the complex structure whose restriction to $Y = T^*N$ is induced by the complex structure on $N$. We prove that the space $\tilde{Y}_J$ admits an algebraic structure and is an affine variety.
