Simplicity of stable principal sheaves

Biswas, Indranil ; Gomez, Tomas L. (2008) Simplicity of stable principal sheaves Bulletin of the London Mathematical Society, 40 (1). pp. 163-171. ISSN 0024-6093

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Let M be a compact connected Kahler manifold, and let G be a connected complex reductive linear algebraic group. We prove that a principal G-sheaf on M admits an admissible Einstein-Hermitian connection if and only if the principal G-sheaf is polystable. Using this it is shown that the holomorphic sections of the adjoint vector bundle of a stable principal G-sheaf on M are given by the center of the Lie algebra of G. The Bogomolov inequality is shown to be valid for polystable principal G-sheaves.

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Source:Copyright of this article belongs to Oxford University Press.
ID Code:3466
Deposited On:12 Oct 2010 04:36
Last Modified:16 May 2016 14:16

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