V. Balaji (Chennai): Principal bundles and the Donaldson-Uhlenbeck compactification
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.