Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations

Autor:	Czapliński, Adam, Krug, Andreas, Lehn, Manfred, Rollenske, Sönke
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: Minor corrections. To appear in Commun. Contemp. Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.11686 Zobrazit plný text záznamu View this record from Arxiv