For a non-singular projective toric variety $X$, the virtual logarithmic Tevelev degrees are defined as the virtual degree of the morphism from the moduli stack of logarithmic stable maps ${\overline{\mathcal{M}}}_{\mathrm{\Gamma }}(X)$ to the product ${\overline{\mathcal{M}}}_{g,n}\times X^n$. In this paper, after proving that Mikhalkin's correspondence theorem holds in genus 0 for logarithmic virtual Tevelev degrees, we use tropical methods to provide closed formulas for the case in which $X$ is a Hirzebruch surface. In order to do so, we explicitly list all the tropical curves contributing to the count.

中文翻译：

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Hirzebruch 表面的属 0 对数和热带固定域计数

对于非奇异射影复曲面簇$X$，虚对数 Tevelev 度定义为来自对数稳定映射的模堆栈的态射的虚拟度${\stackrel{￣}{\mathcal{中号}}}_{\mathrm{\gamma }}（X）$到产品${\stackrel{￣}{\mathcal{中号}}}_{G,n}\times X^n$。在本文中，在证明米哈尔金对应定理在对数虚拟Tevelev度的属0中成立后，我们使用热带方法提供了以下情况的封闭公式：$X$是 Hirzebruch 曲面。为此，我们明确列出了对计数有贡献的所有热带曲线。