Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Adam Czapliński
  • Andreas Krug
  • Manfred Lehn
  • Sönke Rollenske

Research Organisations

External Research Organisations

  • University of Siegen
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Details

Original languageEnglish
Article number2450004
JournalCommunications in Contemporary Mathematics
Volume26
Issue number10
Publication statusPublished - 9 Mar 2024

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.

Keywords

    math.AG

Cite this

Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations. / Czapliński, Adam; Krug, Andreas; Lehn, Manfred et al.
In: Communications in Contemporary Mathematics, Vol. 26, No. 10, 2450004, 09.03.2024.

Research output: Contribution to journal › Article › Research › peer review

Czapliński A, Krug A, Lehn M, Rollenske S. Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations. Communications in Contemporary Mathematics. 2024 Mar 9;26(10):2450004. doi: 10.48550/arXiv.2206.11686, 10.1142/S0219199724500044
Czapliński, Adam ; Krug, Andreas ; Lehn, Manfred et al. / Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations. In: Communications in Contemporary Mathematics. 2024 ; Vol. 26, No. 10.
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