Successive extensions of vector bundles on curves

TL;DR

This paper proves that on a generic curve, bundles formed by successive extensions are stable, and it calculates the dimension of the space of such extensions using degeneration techniques.

Contribution

It introduces a method to analyze stability of bundles obtained through successive extensions on generic curves, including dimension calculations via degeneration.

Findings

Bundles from successive extensions are stable on generic curves.

Dimension of the extension space is explicitly computed.

Degeneration to elliptic chains is used as a key technique.

Abstract

We show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializing the curve to a chain of elliptic components