An Analytic Application of Geometric Invariant Theory

Abstract

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.

Minor modifications

References in corpus (3)

• Polystability and the Hitchin-Kobayashi correspondence
• Construction of the Moduli Space of Higgs Bundles using Analytic Methods
• The Orbit Type Stratification OF the Moduli Space of Higgs Bundles

Cited by in corpus (3)

• An Analytic Application of Geometric Invariant Theory II: Coarse Moduli Spaces
• Group actions on local moduli space of holomorphic vector bundles
• Local structure of the Teichmüller and the Riemann moduli stacks