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arXiv · 1310.7472

Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group

Indranil Biswas·Tomás L. Gómez
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Abstract

We investigate principal $G$-bundles on a compact Kähler manifold, where $G$ is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it is shown that a principal $G$-bundle $E_G$ admits an Einstein-Hermitian connection if and only if $E_G$ is polystable. We give an equivalent formulation of the (semi)stability condition. A question is to compare this definition with that of math.AG/0506511.

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Indranil Biswas, Tomás L. Gómez. 2014-02-12. Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group. https://doi.org/10.3842/sigma.2014.013

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