Autoduality for curves of compact type

TL;DR

This paper proves autoduality for curves of compact type and treelike curves with planar singularities, establishing an isomorphism between their generalized Jacobian and the identity component of the Picard scheme of their compactified Jacobian.

Contribution

It introduces a new autoduality isomorphism for specific classes of singular curves, extending classical results to more complex curve types.

Findings

Autoduality holds for curves of compact type.

An explicit isomorphism between the generalized Jacobian and the Picard scheme is constructed.

The results apply to treelike curves with planar singularities.

Abstract

We prove autoduality for curves of compact type and, more generally, treelike curves with planar singularities. More precisely, we produce an isomorphism between the generalized Jacobian of such a curve and the connected component of the identity of the Picard scheme of the compactified Jacobian of the curve.