仿射涡的分类
Classification of affine vortices
摘要：
我们证明了仿射涡的Hitchin-Kobayashi对应，推广了Jaffe-Taubes关于圆在仿射直线上作用的结果。也就是说，假设紧李群K在Kaehler流形X上有一个Hamilton作用，该流形X是紧的或无穷远凸的，具有一个适当的矩映射，因此对于复化李群G的作用稳定=半稳定。然后，对于某个充分可分的整数n，在具有目标X模规范的K-涡的规范等价类与从加权射影线P（1，n）到X/G的映射类之间存在一个双射，该映射类将无穷远处的堆叠点P（n）映射到X中的半稳定轨迹。这些结果使得伍德沃德的量子Kirwan映射的构造和部分计算成为可能，并在Dimofte、Gukov和Hollande的论文中发挥了作用，这些论文将涡旋数与结不变量联系起来。
英文摘要：
We prove a Hitchin-Kobayashi correspondence for affine vortices generalizing a result of Jaffe-Taubes for the action of the circle on the affine line. Namely, suppose a compact Lie group K has a Hamiltonian action on a Kaehler manifold X which is either compact or convex at infinity with a proper moment map, and so that stable=semistable for the action of the complexified Lie group G. Then, for some sufficiently divisible integer n, there is a bijection between gauge equivalence classes of K-vortices with target X modulo gauge and isomorphism classes of maps from the weighted projective line P(1,n) to X/G that map the stacky point at infinity P(n) to the semistable locus in X. The results allow the construction and partial computation of the quantum Kirwan map in Woodward, and play a role in the conjectures of Dimofte, Gukov, and Hollande relating vortex counts to knot invariants.
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