Rank of divisors on graphs: an algebro-geometric analysis

TL;DR

This paper explores the connection between graph divisor theory and algebraic geometry, proposing an algebro-geometric interpretation of the combinatorial rank and establishing some proofs.

Contribution

It introduces an algebro-geometric perspective on the combinatorial rank of divisors on graphs, linking graph theory with algebraic geometry.

Findings

Proposes an algebro-geometric interpretation of the combinatorial rank.

Establishes proofs of the interpretation in specific cases.

Connects divisor theory on graphs with linear series on algebraic curves.

Abstract

The divisor theory for graphs is compared to the theory of linear series on curves through the correspondence associating a curve to its dual graph. An algebro-geometric interpretation of the combinatorial rank is proposed, and proved in some cases.