Dimensional reduction, SL(2,C)-equivariant bundles and stable holomorphic chains

Details Dimensional reduction, SL(2,C)-equivariant bundles and stable holomorphic chains Dimensional reduction, SL(2,C)-equivariant bundles and stable holomorphic chains

2001-12-16

arxiv.org/abs/math/0112159v1

Int.J.Math. 12 (2001) 159-201

Mathematics

Differential Geometry

43 pages; PDF file can be obtained from http://www.worldscinet.com/journals/ijm/12/1202/S0129167X01000745.html

Scientific paper

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_{i-1}. We then prove a Hitchin-Kobayashi correspondence relating the existence of solutions to certain natural gauge-theoretic 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.

Affiliated with

Also associated with

No associations

Rating

Dimensional reduction, SL(2,C)-equivariant bundles and stable holomorphic chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dimensional reduction, SL(2,C)-equivariant bundles and stable holomorphic chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dimensional reduction, SL(2,C)-equivariant bundles and stable holomorphic chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-621593