Dimensional reduction, SL(2,C)equivariant bundles and stable holomorphic chains
Abstract
In this paper we study gauge theory on SL(2,C)equivariant bundles over XxP^1, where X is a compact Kahler manifold, P^1 is the complex projective line, and the action of SL(2,C) is trivial on X and standard on P^1. We first classify these bundles, showing that they are in correspondence with objects on X  that we call holomorphic chains  consisting of a finite number of holomorphic bundles E_i and morphisms E_i>E_{i1}. We then prove a HitchinKobayashi correspondence relating the existence of solutions to certain natural gaugetheoretic equations and an appropriate notion of stability for an equivariant bundle and the corresponding chain. A central tool in this paper is a dimensional reduction procedure which allow us to go from XxP^1 to X.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2001
 arXiv:
 arXiv:math/0112159
 Bibcode:
 2001math.....12159A
 Keywords:

 Mathematics  Differential Geometry;
 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry;
 58C25 (Primary);
 58A30;
 53C12;
 53C55;
 83C05 (Secondary)
 EPrint:
 43 pages