Linked Hom spaces

TL;DR

This paper develops a theory of linked Hom spaces for chains of vector bundles, providing conditions for their representability and applying it to improve the understanding of limit linear series spaces.

Contribution

It introduces a new framework for linked Hom spaces that complements linked Grassmannians and simplifies the construction of limit linear series spaces.

Findings

Linked Hom spaces are representable by vector bundles under certain conditions.

The new theory offers a clearer construction of limit linear series spaces.

Provides conditions for the homomorphism spaces to be vector bundles.

Abstract

In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain to the other to be itself represented by a vector bundle. We apply this to present a more transparent version of an earlier construction of limit linear series spaces out of linked Grassmannians.