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

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.