圆与黎曼曲面乘积上的奇异厄米特-爱因斯坦单极子
微分几何
2009-10-19 v3 代数几何
摘要
本文证明了圆与黎曼曲面乘积上的奇异幺正厄米特-爱因斯坦单极子的模空间对应于该黎曼曲面上稳定对的模空间。这些对由曲面上的全纯向量丛和该丛的亚纯自同构组成。该自同构的奇点对应于奇异单极子的奇点。随后我们考虑了该模空间的复几何；特别地，我们从复几何和规范理论两个角度计算了其维数。
引用
@article{arxiv.0812.0221,
title = {Singular Hermitian-Einstein monopoles on the product of a circle and a Riemann surface},
author = {Benoit Charbonneau and Jacques Hurtubise},
journal= {arXiv preprint arXiv:0812.0221},
year = {2009}
}
备注
Paper revised for clarity of the arguments. We have now a cleaner and better proof of the irreducibility/stable correspondence, and of the fact that the monopole has the correct weight at the singularity. The construction of the bundle supporting the initial metric under the heat flow is much more explicit