In this paper, we prove that the open Gromov–Witten invariants defined in [20] on K3 surfaces satisfy the Kontsevich–Soibelman wall-crossing formula. One hand, this gives a geometric interpretation of the slab functions in Gross–Siebert program. On the other hands, the open Gromov–Witten invariants coincide with the weighted counting of tropical discs. This is an analog of the corresponding theorem on toric varieties [26][27] but on compact Calabi–Yau surfaces.

中文翻译：

---

K3曲面上全纯圆盘与热带圆盘的对应定理

在本文中，我们证明了在K3曲面上在[20]中定义的开放Gromov–Witten不变量满足Kontsevich–Soibelman墙交叉公式。一方面，这对Gross–Siebert程序中的平板函数进行了几何解释。另一方面，开放的Gromov–Witten不变量与热带盘的加权计数一致。这是复曲面变体上相应定理的一个类似物[26] [27]，但在紧致的Calabi–Yau表面上。