Donaldson-Uhlenbeck type moduli spaces for principal bundles over higher dimensional manifolds

Abstract

We present a compactification of the moduli space of principal $G$-bundles on higher-dimensional complex projective manifolds, which extends the algebro-geometric construction of Balaji of the \it Donaldson--Uhlenbeck \rm compactification. This is achieved by considering semistability calculated with respect to a multipolarization on a projective $n$-fold, consisting of $n-1$ ample integral divisor classes. Moreover, given a curve $C$ that arises as the complete intersection of $(n-1)$ very ample divisors associated with the multipolarization, we construct a modular compactification of the moduli space of principal bundles that are slope-stable with respect to $C$. Furthermore, the geometry of the newly constructed moduli spaces is described by relating them to \it Gieseker \rm moduli spaces.