Linear systems on graphs with a real structure

TL;DR

This paper explores how real structures influence linear systems on graphs and tropical curves, extending classical real curve results to combinatorial and metric graph settings.

Contribution

It introduces the study of real linear systems on graphs with real structures and proves analogous results to classical real curve theory, including generalizations to metric graphs.

Findings

Real linear systems on graphs behave well under real structures

Results analogous to classical real curve theory are established

Extensions to metric graphs and tropical curves are provided

Abstract

A degeneration of a smooth projective curve to a strongly stable curve gives rise to a specialization map from divisors on curves to divisors on graphs. In this paper we show that this specialization behaves well under the presence of real structures. In particular we study real linear systems on graphs with a real structure and we prove results on them comparable to results in the classical theory of real curves. We also consider generalizations to metric graphs and tropical curves.