Linear pencils on graphs and on real curves

TL;DR

This paper explores the relationship between linear systems on algebraic curves and their associated graphs, focusing on linear pencils, and applies these insights to real algebraic curves.

Contribution

It establishes new connections between linear pencils on curves and graphs, providing novel results on pencils on real algebraic curves.

Findings

Derived relations between linear systems on curves and graphs.

Obtained new results on pencils on real curves.

Abstract

A degeneration of curves gives rise to an interesting relation between linear systems on curves and on graphs. In this paper, we consider the case of linear pencils and as an application, we obtain some results on pencils on real curves.