Tensor product of coherent systems

TL;DR

This paper investigates the tensor product of coherent systems on algebraic curves, demonstrating that most known Brill-Noether bundles form alpha-stable systems across all permissible stability parameters.

Contribution

It proves that tensoring known Brill-Noether bundles yields alpha-stable coherent systems for all allowable alpha values.

Findings

Most known Brill-Noether bundles produce alpha-stable systems after tensoring.

The stability holds for all allowable alpha values.

Provides new insights into the structure of stable coherent systems.

Abstract

Let X be a smooth algebraic curve of genus g>=2. A stable vector bundle over X of degree d, rank n with at least k sections is called a Brill-Noether bundle of type (n,d,k). By tensoring coherent systems, we prove that most of the known Brill-Noether bundles define coherent systems of type (n,d,k) that are alpha-stables for all allowable alpha .