Details
| Original language | English |
|---|---|
| Journal | Communications in Contemporary Mathematics |
| Publication status | E-pub ahead of print - 9 Mar 2024 |
Abstract
Keywords
- math.AG
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In: Communications in Contemporary Mathematics, 09.03.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations
AU - Czapliński, Adam
AU - Krug, Andreas
AU - Lehn, Manfred
AU - Rollenske, Sönke
PY - 2024/3/9
Y1 - 2024/3/9
N2 - 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.
AB - 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.
KW - math.AG
U2 - 10.48550/arXiv.2206.11686
DO - 10.48550/arXiv.2206.11686
M3 - Article
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
SN - 0219-1997
ER -