AI 中文总结
本文通过墙函数统一恢复 $K_{\mathbb{P}^2}$ 的闭 Gromov-Witten 不变量与重整化周期，建立 Gross-Siebert 构造到经典枚举镜像对称的直接通道，并给出多项式性定理及热带树和，预期推广至一般 Calabi-Yau 镜像对。
AI 中文摘要
我们通过对一个墙函数进行相同的操作，恢复了 $K_{\mathbb{P}^2}$ 的闭 Gromov-Witten 不变量和重整化镜像周期。这提供了从 Gross-Siebert 构造的内在镜像对到经典枚举镜像对称性的直接通道。其联系在于一个关于穿刺不变量的多项式性定理。假设与归一化板函数的预期识别成立，我们还获得了闭 Gromov-Witten 不变量的有限树和，其以平面热带曲线的类型表示。该机制预计可推广到更一般的 Calabi-Yau 镜像对。
英文摘要
We recover closed Gromov-Witten invariants and renormalized mirror periods for $K_{\mathbb{P}^2}$ by the same operation on a wall function. This gives a direct passage from the Gross-Siebert construction of intrinsic mirror pairs to classical enumerative mirror symmetry. The link is a polynomiality theorem for punctured invariants. Assuming the expected identification with the normalized slab function, we also obtain a finite tree sum for closed Gromov-Witten invariants in terms of types of plane tropical curves. The mechanism is expected to extend to more general Calabi-Yau mirror pairs.
Comments42 pages, 4 figures
