Limits of the trivial bundle on a curve

TL;DR

This paper classifies rank 2 vector bundles on algebraic curves that are limits of trivial bundles, showing they are mostly decomposable except for special cases with indecomposable examples.

Contribution

It provides a complete classification of limit bundles on Brill-Noether generic and hyperelliptic curves, highlighting cases with indecomposable bundles.

Findings

Limit bundles are decomposable on generic and hyperelliptic curves.

Examples of indecomposable limit bundles are constructed for special curves.

The classification is complete for certain classes of curves.

Abstract

We attempt to describe the rank 2 vector bundles on a curve C which are specializations of the trivial bundle. We get a complete classifications when C is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit vector bundles are decomposable. We give examples of indecomposable limit bundles for some special curves.