Correspondence Theorem between Holomorphic Discs and Tropical Discs on K3 Surfaces

2017/03/01 by Yu-Shen Lin, Lin, Yu-Shen · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1703.00411

openalex publication_date 2017/03/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

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 \citeM2\citeNS but on compact Calabi-Yau surfaces.

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