Fibré holomorphes principaux sur une variété kählérienne compacte

Translated title of the contribution: Holomorphic principal bundles over a compact Kähler manifold

Boudjemaâ Anchouche, Hassan Azad, Indranil Biswas

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let p : G → H be a homomorphism between connected reductive algebraic groups over ℂ such that the center of the Lie algebra g is sent to the center of h. If EG is a holomorphic principal G-bundle over a compact connected Kähler manifold M, and EG is semistable (resp. polystable), then the principal H -bundle EG XG H is also semistable (resp. polystable). A G-bundle over M is polystable if and only if it admits an Einstein-Hermitian connection; this is an analog of a theorem of Uhlenbeck and Yau for G-bundles. Two different formulations of the G-bundle analog of the Harder-Narasimhan reduction have been established. The equivalence of the two formulations is a consequence of a group theoretic result.

Original languageFrench
Pages (from-to)109-114
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume330
Issue number2
Publication statusPublished - Jan 15 2000

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ASJC Scopus subject areas

  • Mathematics(all)

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