Extension of structure groups of principal bundles in positive characteristic

Fabrizio Coiai; Yogish I. Holla

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arXiv · math/0312280

Extension of structure groups of principal bundles in positive characteristic

Fabrizio Coiai·Yogish I. Holla

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Abstract

In this article we study the behaviour of semistable principal $G$-bundles over a smooth projective variety $X$ under the extension of structure groups in positive characteristic. We extend some results of Ramanan-Ramanathan \cite{Ramanan-Ramanathan} on rationality of instability flags and show that the associated vector bundles via representations of $G$ are not too unstable and the instability can be bounded by a constant independent of semistable bundles. As a consequence of this the boundedness of the set of isomorphism classes of semistable $G$-bundles with fixed degree and Chern classes is proven.

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BibTeX RIS

Fabrizio Coiai, Yogish I. Holla. 2004-08-03. Extension of structure groups of principal bundles in positive characteristic. https://arxiv.org/abs/math/0312280

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