Kobayashi-Hitchin correspondence for analytically stable bundles

Abstract

We prove the existence of a Hermitian-Einstein metric on holomorphic vector bundles with a Hermitian metric satisfying the analytic stability condition, under some assumption for the underlying Kähler manifolds. We also study the curvature decay of the Hermitian-Einstein metrics. It is useful for the study of the classification of instantons and monopoles on the quotient of $4$-dimensional Euclidean space by some types of closed subgroups. We also explain examples of doubly periodic monopoles corresponding to some algebraic data.

More explanations are included. Some minor mistakes are corrected

References in corpus (3)

• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules
• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
• Spatially periodic instantons: Nahm transform and moduli

Cited by in corpus (2)

• Multiplicative Hitchin Systems and Supersymmetric Gauge Theory
• Higgs bundles over non-compact Gauduchon manifolds