Extension of structure groups of principal bundles in positive characteristic

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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.
25 pages. To appear in the J. Reine Angew. Math

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Algebraic Geometry, 14J60;14L24

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http://salesiana.dossiersoluciones.com/handle/123456789/69601

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312280
 http://arxiv.org/abs/math/0312280

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arXiv