DIMENSIONAL REDUCTION, SL(2,C)-EQUIVARIANT BUNDLES AND STABLE HOLOMORPHIC CHAINS
DIMENSIONAL REDUCTION, SL(2,C)-EQUIVARIANT BUNDLES AND STABLE HOLOMORPHIC CHAINS
复制标题
DOI：
--
复制
发表时间：
2001-12
期刊：
影响因子：
--
通讯作者：
Luis 'Alvarez-C'onsul;O. Garc'ia-Prada
中科院分区：
文献类型：
--
作者：
Luis 'Alvarez-C'onsul;O. Garc'ia-Prada
本文研究了SL(2，C)-等变束overX×P 1上的规范理论，其中X是紧的Kahler流形，p1是复射影线，SL（2，C）在X上的作用是平凡的，在p1上的作用是标准的。我们首先对这些束进行分类，证明它们对应于x上的对象-我们称之为全纯链-由有限数量的全纯束Ei和morphismei→Ei 1组成。然后，我们证明了关于某些自然规范理论方程解的存在性的Hitchin-Kobayashi对应关系，以及等变束和相应链的稳定性的适当概念。本文中的一个中心工具是一个降维程序，它允许我们访问fromX×P 1 toX。
In this paper we study gauge theory on SL(2,C)-equivariant bundles overX×P 1 ,w here 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 onX — that we call holomorphic chains — consisting of a finite number of holomorphic bundles Ei and morphismsEi →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 fromX×P 1 toX.