U(1)-vortices and quantum Kirwan map

Abstract

We study the symplectic vortex equation over the complex plane, for the target space ${\mathbb{C}}^N$ ($N\ge 2$) with diagonal U(1)-action. We classify all solutions with finite energy and identify their moduli spaces, which generalizes Taubes' result for N=1. We also studied their compactifications and use them to compute the associated quantum Kirwan maps ${\kappa }_Q:H_{U(1)}^{\ast }({\mathbb{C}}^N)\to Q{H}^{\ast }({\mathbb{P}}^{N-1})$.

arXiv comment30 pages, 2 figures