Simplicity of stable principal sheaves | Zendy

Biswas Indranil | Zendy; Gómez Tomás L. | Zendy

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Simplicity of stable principal sheaves

Author(s) -

Biswas Indranil,

Gómez Tomás L.

Publication year - 2008

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdm116

Subject(s) - mathematics , sheaf , pure mathematics , principal bundle , holomorphic function , vector bundle , principal (computer security) , algebraic group , hermitian matrix , linear algebraic group , complex manifold , connection (principal bundle) , algebra over a field , algebraic number , mathematical analysis , geometry , computer science , operating system

Let M be a compact connected Kähler 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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