Degeneration of Linear Series From the Tropical Point of View and Applications

TL;DR

This survey explores the theory of linear series on tropical curves, connecting tropical and classical algebraic geometry, highlighting recent advances and applications in Brill-Noether and arithmetic geometry.

Contribution

It provides a comprehensive overview of tropical linear series, detailing key techniques and recent developments with a focus on their applications in algebraic geometry.

Findings

Tropical linear series relate closely to classical algebraic geometry.

Recent advances have expanded applications in Brill-Noether theory.

The survey highlights new methods and results in the field.

Abstract

In this survey, we discuss linear series on tropical curves and their relation to classical algebraic geometry, describe the main techniques of the subject, and survey some of the recent major developments in the field, with an emphasis on applications to problems in Brill-Noether theory and arithmetic geometry.