On the Tropical Discs Counting on Elliptic K3 Surfaces with General Singular Fibres

2017/10/29 by Yu-Shen Lin, Lin, Yu-Shen
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Polynomial and algebraic computation #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1710.10625

openalex publication_date 2017/10/29 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

Using Lagrangian Floer theory, we study the tropical geometry of K3 surfaces with general singular fibres. In particular, we give the local models for the type I_n, II, III and IV singular fibres in the Kodaira's classification and generalize the correspondence theorem between open Gromov-Witten invariants/tropical discs counting to these cases.

Related

• Correspondence Theorem between Holomorphic Discs and Tropical Discs on K3 Surfaces
• Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing
• Distinguished bases in the wrapped Floer cohomology of tropical Lagrangian surfaces
• Enumerative Geometry of Del Pezzo Surfaces
• Counting curves on Hirzebruch surfaces: tropical geometry and the Fock\n space