论文标题
格罗莫夫（Gromov）理论通过根和对数
Gromov-Witten theory via roots and logarithms
论文作者
论文摘要
Orbifold和对数结构为简单的正常交叉对$（x | d）$的曲线虚拟枚举提供了独立的路线。这些理论并不重合，他们的关系仍然神秘。我们证明，零（x | d）$的多根爆炸的多根堆栈的Orbifold属理论收敛到$（x | d）$的相应对数理论。有了固定的数值数据，有一个明确的组合标准可以保证当爆炸充分完善以使理论重合时。证明中有两个关键想法。首先是构建天真的格罗莫夫 - 理论，该理论是根和对数之间的中介。第二个是热带稳定地图的平滑定理。然后，几何定理通过虚拟相交理论相对于通用目标遵循。结果将新的计算工具导入对数Gromov-Witten理论。作为一种应用，我们表明，零属的对数Gromov-witten理论由其地层的绝对Gromov-witten理论决定。
Orbifold and logarithmic structures provide independent routes to the virtual enumeration of curves with tangency orders for a simple normal crossings pair $(X|D)$. The theories do not coincide and their relationship has remained mysterious. We prove that the genus zero orbifold theories of multi-root stacks of strata blowups of $(X|D)$ converge to the corresponding logarithmic theory of $(X|D)$. With fixed numerical data, there is an explicit combinatorial criterion that guarantees when a blowup is sufficiently refined for the theories to coincide. There are two key ideas in the proof. The first is the construction of a naive Gromov-Witten theory, which serves as an intermediary between roots and logarithms. The second is a smoothing theorem for tropical stable maps; the geometric theorem then follows via virtual intersection theory relative to the universal target. The results import new computational tools into logarithmic Gromov-Witten theory. As an application, we show that the genus zero logarithmic Gromov-Witten theory of a pair is determined by the absolute Gromov-Witten theories of its strata.
