Limit linear series and tropical divisors on chains

TL;DR

This paper explores the relationship between limit linear series on chains of elliptic curves and tropical divisors on chains, providing combinatorial tools to compute invariants in Brill-Noether theory.

Contribution

It introduces effective limit linear series and compares algebraic and tropical models for analyzing linear series on chains.

Findings

Equivalence between algebraic and tropical models for limit linear series

Introduction of effective limit linear series

Computational methods for Brill-Noether invariants

Abstract

We describe the space of Eisenbud-Harris limit linear series on a chain of elliptic curves and compare it with the theory of divisors on tropical chains. Either model allows to compute some invariants of Brill-Noether theory using combinatorial methods. We introduce effective limit linear series.