An analytic application of Geometric Invariant Theory

JOURNAL OF GEOMETRY AND PHYSICS

卷:165

Article

Buchdahl, Nicholas¹  Schumacher, Georg² 

[1] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

[2] Philipps Univ Marburg, Fachbereich Math & Informat, Hans Meerwein Str, D-35032 Marburg, Germany

关键词: Analytic GIT-quotients;    Polystable vector bundles on compact;    Kahler manifolds;    Hermite-Einstein connections;    Moduli spaces;   

DOI  :  10.1016/j.geomphys.2021.104237

来源: Elsevier

【 摘 要 】

Given a compact Kahler 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 Kahler 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. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free