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摘要翻译：
本文探讨了有理后代Gromov-Witten不变量的代数几何理论在多大程度上可以推广到热带世界。尽管我们使用的热带模空间是不紧凑的，但答案出人意料地是肯定的。我们讨论了弦方程、除数方程和dilaton方程，证明了一个用“边界”除数描述交集的分裂引理，并证明了WDVV Resp的一般热带版本。拓扑递推方程（在某些假设下）。作为一个直接应用，我们证明了toric变体$\mathbb{P}^1$，$\mathbb{P}^2$，$\mathbb{P}^1\乘以mathbb{P}^1$和psi-条件仅结合点条件时，热带和经典后代Gromov-Witten不变量重合（扩展了Markwig-Rau-2008中$\mathbb{P}^2$的结果）。我们的方法利用热带交集理论，可以统一和简化现有的热带枚举几何（对于有理曲线）的某些部分。
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英文标题：
《Intersections on tropical moduli spaces》
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作者：
Johannes Rau
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最新提交年份：
2015
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
This article explores to which extent the algebro-geometric theory of rational descendant Gromov-Witten invariants can be carried over to the tropical world. Despite the fact that the tropical moduli-spaces we work with are non-compact, the answer is surprisingly positive. We discuss the string, divisor and dilaton equations, we prove a splitting lemma describing the intersection with a "boundary" divisor and we prove general tropical versions of the WDVV resp. topological recursion equations (under some assumptions). As a direct application, we prove that the toric varieties $\mathbb{P}^1$, $\mathbb{P}^2$, $\mathbb{P}^1 \times \mathbb{P}^1$ and with Psi-conditions only in combination with point conditions, the tropical and classical descendant Gromov-Witten invariants coincide (which extends the result for $\mathbb{P}^2$ in Markwig-Rau-2008). Our approach uses tropical intersection theory and can unify and simplify some parts of the existing tropical enumerative geometry (for rational curves).
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PDF链接：
https://arxiv.org/pdf/0812.3678
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