论文标题
双Hurwitz数字：多项式，拓扑递归和交点理论
Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
论文作者
论文摘要
双Hurwitz编号列举了$ \ mathbb {cp}^1 $的分支封面，并在两个点上有规定的分支，在其他地方简单的分支。与单个情况相反，它们的基本几何形状尚不清楚。在第二名和第三名作者的先前工作中，双重赫维兹的数字被猜想是为了满足多项式结构，并受拓扑结构的控制，类似于现有的结果。在本文中，我们通过仔细分析半hurwitz数字的半罚款楔形表示来解决这些猜想，通过推动以前用于其他Hurwitz问题的进一步方法。我们通过将Johnson-Pandharipande-tseng公式用于Orbifold Hurwitz数字，并使用光谱曲线变化的拓扑结构属性来推断出针对双Hurwitz数字的ELSV样公式的初步版本。在此分析过程中，我们推出了Chiodo类的某些消失特性。
Double Hurwitz numbers enumerate branched covers of $\mathbb{CP}^1$ with prescribed ramification over two points and simple ramification elsewhere. In contrast to the single case, their underlying geometry is not well understood. In previous work by the second- and third-named authors, the double Hurwitz numbers were conjectured to satisfy a polynomiality structure and to be governed by the topological recursion, analogous to existing results concerning single Hurwitz numbers. In this paper, we resolve these conjectures by a careful analysis of the semi-infinite wedge representation for double Hurwitz numbers, by pushing further methods previously used for other Hurwitz problems. We deduce a preliminary version of an ELSV-like formula for double Hurwitz numbers, by deforming the Johnson-Pandharipande-Tseng formula for orbifold Hurwitz numbers and using properties of the topological recursion under variation of spectral curves. In the course of this analysis, we unveil certain vanishing properties of the Chiodo classes.
