Approximate Hermitian-Yang-Mills structures on semistable principal Higgs bundles

Abstract

We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.

16 pages, appears in Ann. Glob. Anal. Appl. 2014. arXiv admin note: text overlap with arXiv:0905.2870

References in corpus (3)

• Yang-Mills equation for stable Higgs sheaves
• Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures
• Existence of approximate Hermitian-Einstein structures on semistable principal bundles

Cited by in corpus (1)

• Non-existence of Higgs fields on Calabi-Yau Manifolds