Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913186146418688 |
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| author | Czapliński, Adam Krug, Andreas Lehn, Manfred Rollenske, Sönke |
| author_facet | Czapliński, Adam Krug, Andreas Lehn, Manfred Rollenske, Sönke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11686 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations Czapliński, Adam Krug, Andreas Lehn, Manfred Rollenske, Sönke Algebraic Geometry 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. |
| title | Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2206.11686 |