Automorphisms and connections on Higgs bundles over compact Kähler manifolds

Indranil Biswas, Steven B. Bradlow, Adam Jacob, Matthias Stemmler

Research output: Contribution to journalArticlepeer-review


Let (E,φ) be a Higgs vector bundle over a compact connected Kähler manifold X. Fix any filtration of E by coherent analytic subsheaves in which each sheaf is preserved by the Higgs field, and each successive quotient is a torsionfree and stable Higgs sheaf. Denote by G the direct sum of these stable quotients, and let the singular set of G be called S ⊂ X. We construct a 1-parameter family of filtration preserving C ∞ isomorphisms Φt:G|XS→E|XS, and a Hermitian metric h on G|X\S, such that as t → + ∞ , the Chern connection for the Hermitian Higgs bundle (Φt*E,Φt*φ,h)|X\S converges, in the C ∞ Fréchet topology over any relatively compact open subset of X \ S, to the direct sum of the Yang-Mills-Higgs connections on the direct summands in G.We also prove an analogous result for principal Higgs G-bundles on X.

Original languageEnglish (US)
Pages (from-to)139-152
Number of pages14
JournalDifferential Geometry and its Application
Issue number1
StatePublished - Feb 2014


  • 32L05
  • 53C07
  • Approximate Yang-Mills-Higgs connection
  • Automorphism
  • Higgs bundle

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics


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