Translator Disclaimer
January 2021 Correspondence theorem between holomorphic discs and tropical discs on K3 surfaces
Yu-Shen Lin
Author Affiliations +
J. Differential Geom. 117(1): 41-92 (January 2021). DOI: 10.4310/jdg/1609902017

Abstract

In this paper, we prove that the open Gromov–Witten invariants defined in [20] on K3 surfaces satisfy the Kontsevich–Soibelman wall-crossing formula. 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 [26][27] but on compact Calabi–Yau surfaces.

Citation

Download Citation

Yu-Shen Lin. "Correspondence theorem between holomorphic discs and tropical discs on K3 surfaces." J. Differential Geom. 117 (1) 41 - 92, January 2021. https://doi.org/10.4310/jdg/1609902017

Information

Received: 8 May 2017; Published: January 2021
First available in Project Euclid: 6 January 2021

MathSciNet: MR4195752
Digital Object Identifier: 10.4310/jdg/1609902017

Rights: Copyright © 2021 Lehigh University

JOURNAL ARTICLE
52 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.117 • No. 1 • January 2021
Back to Top