论文标题
延长的ADE曲线和拉格朗日纤维的压缩雅各布人
Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations
论文作者
论文摘要
我们观察到，K3表面上足够正线性系统中的一般还原曲线具有一种形式，可以概括Kodaira对奇异椭圆纤维的分类，因此称它们为扩展的ADE曲线。 在这样的曲线$ c $上，我们描述了一个压实的雅各布式，并表明其组件反映了$ c $的相交图。当$ c $减少时，这会扩展已知的结果，但是当$ c $未降低时，会出现新的困难。作为应用程序，我们获得了Beauville-Mukai类型某些拉格朗日纤维的一般单数纤维的明确描述。
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.
