Specialization of linear systems from curves to graphs

TL;DR

This paper explores how linear systems on algebraic curves relate to those on graphs, with applications spanning graph theory, arithmetic geometry, and tropical geometry, highlighting the specialization process of divisors.

Contribution

It introduces a framework connecting linear systems on curves and graphs, extending the theory to new contexts and applications.

Findings

Established a correspondence between linear systems on curves and graphs.

Demonstrated applications to tropical and arithmetic geometry.

Provided new insights into divisor specialization processes.

Abstract

We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and tropical geometry.