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.

给定一个紧凑的Kähler流形，应用几何不变理论构造解析GIT商，该商是将（多）稳定全纯矢量束的空间分类为局部模型的模型，该稳定束包含稳定束的粗模空间作为开放子空间。对于局部模型，参数空间上存在不变的广义Weil-Petersson形式，这是辛形式对光滑环境空间的限制。如果下面的Kähler流形是Hodge型的，则已知稳定向量束的模空间上的Weil-Petersson形式是某些装有Quillen度量的行列式束的Chern形式。它在分类GIT空间上产生了全纯线束以及连续的Hermitian度量。