Gromov-Witten theory with maximal contacts
Gromov-Witten theory with maximal contacts
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具有最大接触的 Gromov-Witten 理论
DOI：
10.1017/fms.2021.78
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Nabijou N
中科院分区：
文献类型：
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作者：
Nabijou N
我们提出了一种交点理论方法，在正数存在的情况下，将0格对数Gromov-Witten理论中的问题约简为光滑对的Gromov-Witten理论中的问题。将该方法应用于沿简单法向交叉除数的最大接触阶有理曲线的枚举几何，并解决了其与局部曲线计数的关系问题。得到了三个结果。我们给出了van Garrel-Graber-Ruddat和seng - you的局部对数猜想的反例。我们证明了该猜想的一个弱形式对乘积几何成立。最后，根据已知的有效算法的相对不变量，我们明确地确定了局部理论和对数理论之间的区别。地图热带模的多面体几何在分析中起着重要而复杂的作用。
We propose an intersection-theoretic method to reduce questions in genus 0 logarithmic Gromov–Witten theory to questions in the Gromov–Witten theory of smooth pairs, in the presence of positivity. The method is applied to the enumerative geometry of rational curves with maximal contact orders along a simple normal crossings divisor and to recent questions about its relationship to local curve counting. Three results are established. We produce counterexamples to the local-logarithmic conjectures of van Garrel–Graber–Ruddat and Tseng–You. We prove that a weak form of the conjecture holds for product geometries. Finally, we explicitly determine the difference between local and logarithmic theories, in terms of relative invariants for which efficient algorithms are known. The polyhedral geometry of the tropical moduli of maps plays an essential and intricate role in the analysis.