Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations

authored by

Adam Czapliński, Andreas Krug, Manfred Lehn, Sönke Rollenske

Abstract

We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalises Kodaira's classification of singular elliptic fibres and thus call them extended ADE curves. On such a curve \(C\), we describe a compactified Jacobian and show that its components reflect the intersection graph of \(C\). This extends known results when \(C\) is reduced, but new difficulties arise when \(C\) is non-reduced. As an application, we get an explicit description of general singular fibres of certain Lagrangian fibrations of Beauville-Mukai type.

Organisation(s)

Institute of Algebraic Geometry

External Organisation(s)

University of Siegen

Type

Article

Journal

Communications in Contemporary Mathematics

Volume

26

ISSN

0219-1997

Publication date

09.03.2024

Publication status

Published

Peer reviewed

Yes

Electronic version(s)

https://doi.org/10.48550/arXiv.2206.11686 (Access: Open)
https://doi.org/10.1142/S0219199724500044 (Access: Closed)