The vortex equation on affine manifolds
Differential Geometry
2013-04-18 v1
Abstract
Let M be a compact connected special affine manifold equipped with an affine Gauduchon metric. We show that a pair (E, \phi), consisting of a flat vector bundle E over M and a flat nonzero section \phi\ of E, admits a solution to the vortex equation if and only if it is polystable. To prove this, we adapt the dimensional reduction techniques for holomorphic pairs on K\"ahler manifolds to the situation of flat pairs on affine manifolds.
Keywords
Cite
@article{arxiv.1304.4727,
title = {The vortex equation on affine manifolds},
author = {Indranil Biswas and John Loftin and Matthias Stemmler},
journal= {arXiv preprint arXiv:1304.4727},
year = {2013}
}
Comments
18 pages, Transactions of the American Mathematical Society (to appear)