We study the stationary descendant Gromov–Witten theory of toric surfaces by combining and extending a range of techniques – tropical curves, floor diagrams and Fock spaces. A correspondence theorem is established between tropical curves and descendant invariants on toric surfaces using maximal toric degenerations. An intermediate degeneration is then shown to give rise to floor diagrams, giving a geometric interpretation of this well-known bookkeeping tool in tropical geometry. In the process, we extend floor diagram techniques to include descendants in arbitrary genus. These floor diagrams are then used to connect tropical curve counting to the algebra of operators on the bosonic Fock space, and are showno coincide with the Feynman diagrams of appropriate operators. This extends work of a number of researchers, including Block–Göttsche, Cooper–Pandharipande and Block–Gathmann–Markwig.

中文翻译：

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计算 Hirzebruch 曲面上的曲线：热带几何和 Fock 空间

我们通过结合和扩展一系列技术——热带曲线、楼层图和 Fock 空间来研究复曲面的静止后裔 Gromov-Witten 理论。使用最大复曲面退化，在复曲面上的热带曲线和后代不变量之间建立了对应定理。然后显示中间退化以产生楼层图，对热带几何学中这个著名的簿记工具进行几何解释。在此过程中，我们扩展了楼层图技术以包括任意属的后代。然后这些楼层图用于将热带曲线计数与玻色子 Fock 空间上的算子代数联系起来，并显示出与适当算子的费曼图一致。这扩展了包括 Block-Göttsche 在内的许多研究人员的工作，