Generalized Jacobians of graphs

Paper

Abstract

We define a generalized Jacobian

and a generalized Picard group

of a graph

with respect to a modulus

with

vertices of

and

. These groups occur as the component groups of Néron models of generalized Jacobians. We prove a universal mapping property for

and show that an Abel-Jacobi map in this context induces an isomorphism from

. We also reinterpret

in terms of sheaves on the geometric realization

, making a connection with tropical geometry.