Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification

Details Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification

2005-05-06

arxiv.org/abs/math/0505106v1

Mathematics

Algebraic Geometry

46 pages

Scientific paper

Let $H$ be a semisimple algebraic group. We prove the semistable reduction theorem for $\mu$--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 $\mu$--semistable principal $H$--bundles with fixed characteristic classes and describe its points. For large characteristic classes we show that the moduli space of $\mu$--stable principal $H$--bundles is non--empty.

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