Correspondence Theorem between Holomorphic Discs and Tropical Discs on K3 Surfaces
Symplectic Geometry
2017-12-05 v2 Algebraic Geometry
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.
Cite
@article{arxiv.1703.00411,
title = {Correspondence Theorem between Holomorphic Discs and Tropical Discs on K3 Surfaces},
author = {Yu-Shen Lin},
journal= {arXiv preprint arXiv:1703.00411},
year = {2017}
}
Comments
59 pages, 4 figures. Comments are welcome