Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification

V. Balaji

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Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification

V. Balaji

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Abstract

Let $H$ be a semisimple algebraic group. We prove the semistable reduction theorem for $μ$--semistable principal $H$--bundles over a {\it smooth projective variety $X$} defined over the field $\bc$. When $X$ is a {\it smooth projective surface} and $H$ is simple, we construct the algebro--geometric Donaldson--Uhlenbeck compactification of the moduli space of $μ$--semistable principal $H$--bundles with fixed characteristic classes and describe its points. For large characteristic classes we show that the moduli space of $μ$--stable principal $H$--bundles is non--empty.

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BibTeX RIS

V. Balaji. 2005-05-06. Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification. https://arxiv.org/abs/math/0505106

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