Correspondence Theorem between Holomorphic Discs and Tropical Discs on K3 Surfaces

Abstract

We prove that the open Gromov-Witten invariants on K3 surfaces satisfy the Kontsevich-Soibelman wall-crossing formula. One 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 \cite{M2}\cite{NS} but on compact Calabi-Yau surfaces.

59 pages, 4 figures. Comments are welcome

References in corpus (1)

• BPS Wall Crossing and Topological Strings

Cited by in corpus (2)

• K3 metrics from little string theory
• On the Complex Affine Structures of SYZ Fibration of Del Pezzo Surfaces