Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations

verfasst von

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.

Organisationseinheit(en)

Institut für Algebraische Geometrie

Externe Organisation(en)

Universität Siegen

Typ

Artikel

Journal

Communications in Contemporary Mathematics

Band

26

ISSN

0219-1997

Publikationsdatum

09.03.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2206.11686 (Zugang: Offen)
https://doi.org/10.1142/S0219199724500044 (Zugang: Geschlossen)