论文标题
几何不变理论的分析应用
An Analytic Application of Geometric Invariant Theory
论文作者
论文摘要
鉴于紧凑的Kähler歧管，几何不变理论被应用于构造分析性GIT品质，它们是（poly）稳定的全态矢量束的局部模型，该模型包含包含稳定捆绑包的粗模量空间作为开放子空间。对于本地模型，不变的广义Weil-Petersson形式存在于参数空间上，这是光滑环境空间上符号形式的限制。如果基本的kähler歧管是霍奇类型，则众所周知，稳定矢量捆绑包的模量空间上的weil-petersson形式是配备quillen度量的特定决定性线束的Chern形式。它与连续的Hermitian指标一起在分类的GIT空间上产生了全体形状线束。
Given a compact Kähler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of stable bundles as an open subspace. For local models invariant generalized Weil-Petersson forms exist on the parameter spaces, which are restrictions of symplectic forms on smooth ambient spaces. If the underlying Kähler manifold is of Hodge type, then the Weil-Petersson form on the moduli space of stable vector bundles is known to be the Chern form of a certain determinant line bundle equipped with a Quillen metric. It gives rise to a holomorphic line bundle on the classifying GIT space together with a continuous hermitian metric.
