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Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations

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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, moduli of stable sheaves, linear systems on K3 surfaces, Lagrangian fibrations, Compactified Jacobians, sheaves on singular curves

ASJC Scopus subject areas

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 journalArticleResearchpeer 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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