Decomposition of Lagrangian classes on \(K3\) surfaces
type: Item
instance of: scholarly article
title: Decomposition of Lagrangian classes on \(K3\) surfaces
zbMATH Open document ID: 1498.14100
author: Kuan-Wen Lai
author: Yu-Shen Lin
author: Luca Schaffler
published in: Mathematical Research Letters
publication date: 2022-08-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/2001.00202
review text: The aim of the paper under review is to study a \(K3\) surface \(X\) together with a (Ricci-flat) Kähler form on \(X\). The main question is under what condition any Lagrangian class is special. The first part is devoted to giving criteria for it to happen when a Kähler form is given on \(X\). More precisely, if there exists a Lagrangian class of positive self-intersection, then, any Lagrangian is special, and otherwise, it is not the case, but any Lagrangian is special if and only if there exists a negative-definite lattice \(N\) such that both the Lagrangian and special Lagrangian lattices contain \(N\). In the second part, the authors turn to a study in deformation of Kähler forms on \(X\), and show that there exists a dense subset \(\mathcal{S}_X\) of the Kähler cone of \(X\) such that for any class in \(\mathcal{S}_X\), any associated Lagrangian is special. Finally, the authors conclude by describing possible special Lagrangian fibrations on \(X\).
reviewed by: Makiko Mase
Mathematics Subject Classification ID: 14J28
zbMATH DE Number: 7579210
zbMATH Keywords: Lagrangian classes on a Kähler \(K3\) surface
MaRDI profile type: Publication
arXiv ID: 2001.00202
OpenAlex ID: W4293483146
DOI: 10.4310/MRL.2021.V28.N6.A5
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description: scientific article