论文标题
稳定的地图到looijenga对
Stable maps to Looijenga pairs
论文作者
论文摘要
具有最大边界或looijenga对的log calabi-yau表面是一对$（y，d）$，带有$ y $ $ y $ a平滑的理性投射复合物表面和$ d = d_1 + \ dots + d_l \ in | k_y | -k_y | $在两人的某些积极条件下，我们提出了一系列信件，将五个不同类别的枚举不变性与$（y，d）$：： 1）$（y，d）$的log gromov-witten理论， 2）$ \ bigoplus_i \ mathcal {o} _y（-d_i）$，$ \ bigoplus_i \ gromov-witten理论 3）在$（y，d）$确定的3倍的卡拉比（Calabi-yau 4）$（y，d）$和 5）KLEMM-PANDHARIPANDE，IONEL-PARKER和LABASTIDA-MARINO-OOGURI-VAFA在不同情况下考虑的一类BPS不变性。 此外，我们为所有这些不变的计算提供了完整的封闭式解决方案。
A log Calabi-Yau surface with maximal boundary, or Looijenga pair, is a pair $(Y,D)$ with $Y$ a smooth rational projective complex surface and $D=D_1+\dots + D_l \in |-K_Y|$ an anticanonical singular nodal curve. Under some positivity conditions on the pair, we propose a series of correspondences relating five different classes of enumerative invariants attached to $(Y,D)$: 1) the log Gromov-Witten theory of the pair $(Y,D)$, 2) the Gromov-Witten theory of the total space of $\bigoplus_i \mathcal{O}_Y(-D_i)$, 3) the open Gromov-Witten theory of special Lagrangians in a Calabi-Yau 3-fold determined by $(Y,D)$, 4) the Donaldson-Thomas theory of a symmetric quiver specified by $(Y,D)$, and 5) a class of BPS invariants considered in different contexts by Klemm-Pandharipande, Ionel-Parker, and Labastida-Marino-Ooguri-Vafa. We furthermore provide a complete closed-form solution to the calculation of all these invariants.
