离散可采纳覆盖的热带循环

本文应用前述工作中开发的技术框架来离散可采纳覆盖及其模数空间。更准确地说，我们在固定目标的genus、标记腿的数量以及这些标记腿上的规制ramification轮廓后，构建了一个参数化离散可采纳覆盖的poic-space。我们 then construct a linear poic-fibration over this poic-space and show that the usual weight assignment of covers produces an equivariant cycle of this poic-fibration。这个poic-fibration天然地具有source和target maps，after taking the weak pushforward in top dimension through the source map and subsequently forgetting the marking, this gives rise to an equivariant tropical cycle of the corresponding spanning tree fibration。通过这个 framework 我们获得了先前已知结果的推广，这些结果涉及tropical curves的gonality。这些热带循环的特殊案例yield the following result: \emph{A generic genus-$g$ $r$-marked tropical curve $\Gamma$ (with $g+r$ even) has $C_{\frac{g+r}{2}}$ many $r$-marked discrete admissible covers of degree $\frac{g+r}{2}+1$ of a tree (counted with multiplicity) that have a tropical modification of $\Gamma$ as a source, where $C_{\frac{g+r}{2}}$ is the $(\frac{g+r}{2})$th Catalan number}。