Decomposition of Lagrangian classes on K3 surfaces
Differential Geometry
2022-08-16 v3 Algebraic Geometry
Abstract
We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in terms of lattice theory. As a result, we prove the decomposability on an arbitrary K3 surface with respect to the K\"ahler classes in dense subsets of the K\"ahler cone. Using the same technique, we show that the K\"ahler classes on a K3 surface which admit a special Lagrangian fibration form a dense subset also. This implies that there are infinitely many special Lagrangian 3-tori in any log Calabi-Yau 3-fold.
Cite
@article{arxiv.2001.00202,
title = {Decomposition of Lagrangian classes on K3 surfaces},
author = {Kuan-Wen Lai and Yu-Shen Lin and Luca Schaffler},
journal= {arXiv preprint arXiv:2001.00202},
year = {2022}
}
Comments
24 pages. Final version. To appear in Mathematical Research Letters