Mirror curve of orbifold Hurwitz numbers
Mirror curve of orbifold Hurwitz numbers
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发表时间：
2019-04
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通讯作者：
Olivia Dumitrescu;M. Mulase
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作者：
Olivia Dumitrescu;M. Mulase
边收缩运算是解决各种图计数问题的有效工具，例如计算Grothendieck的dessins d 'enfants和简单和双重Hurwitz数。这些计数问题可以通过称为拓扑递归的机制来解决，拓扑递归是对应于这些计数问题的镜像B模型。我们表明，对于orbifold Hurwitz数的情况下，镜像对象，即，谱曲线及其上的微分形式仅由亏格为0的计数问题的边收缩运算和一个标记点构成。这形成了与Gromov-Witten理论的平行，其中亏格0 Gromov-Witten不变量对应于镜像B模型全纯几何。
Edge-contraction operations form an effective tool in various graph enumeration problems, such as counting Grothendieck's dessins d'enfants and simple and double Hurwitz numbers. These counting problems can be solved by a mechanism known as topological recursion, which is a mirror B-model corresponding to these counting problems. We show that for the case of orbifold Hurwitz numbers, the mirror objects, i.e., the spectral curve and the differential forms on it, are constructed solely from the edge-contraction operations of the counting problem in genus $0$ and one marked point. This forms a parallelism with Gromov-Witten theory, where genus 0 Gromov-Witten invariants correspond to mirror B-model holomorphic geometry.