## Journal of Differential Geometry

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

V. Balaji

#### Abstract

Let $H$ be a semisimple algebraic group. We prove the semistable reduction theorem for $\mu$-semistable principal $H$-bundles over a smooth projective variety $X$ defined over the field C. When $X$ is a 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.

#### Article information

Source
J. Differential Geom., Volume 76, Number 3 (2007), 351-398.

Dates
First available in Project Euclid: 25 May 2007

https://projecteuclid.org/euclid.jdg/1180135692

Digital Object Identifier
doi:10.4310/jdg/1180135692

Mathematical Reviews number (MathSciNet)
MR2331525

Zentralblatt MATH identifier
1121.14037

#### Citation

Balaji, V. Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification. J. Differential Geom. 76 (2007), no. 3, 351--398. doi:10.4310/jdg/1180135692. https://projecteuclid.org/euclid.jdg/1180135692