2022/06/23 by Czapliński, Adam, Krug, Andreas, Lehn, Manfred +1
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2206.11686
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.