Moduli of Crude Limit Linear Series

TL;DR

This paper investigates the relationship between Eisenbud-Harris and Osserman's spaces of limit linear series, providing a characterization of when crude limit linear series form an open subset in Osserman's compactification.

Contribution

It offers a complete characterization of when crude limit linear series contain an open subset of Osserman's space, advancing the understanding of limit linear series compactifications.

Findings

Crude limit linear series form an open subset in Osserman's space under specific conditions.

The paper provides criteria for the density of refined limit linear series in different spaces.

It clarifies the relationship between Eisenbud-Harris and Osserman's constructions.

Abstract

Eisenbud and Harris introduced the theory of limit linear series, and constructed a space parametrizing their limit linear series. Recently, Osserman introduced a new space which compactifies the Eisenbud-Harris construction. In the Eisenbud-Harris space, the set of refined limit linear series is always dense on a general reducible curve. Osserman asks when the same is true for his space. In this paper, we answer his question by characterizing the situations when the crude limit linear series contain an open subset of his space.