On $(k,l)$-stable vector bundles over algebraic curves

TL;DR

This paper investigates $(k,l)$-stable vector bundles on algebraic curves, exploring their properties, relations with stability and Segre invariants, and providing explicit descriptions for ranks 2 and 3, linking to Brill-Noether loci.

Contribution

It offers a detailed analysis of $(k,l)$-stability, connecting it with classical stability, Segre invariants, and Brill-Noether theory, with explicit descriptions for low ranks.

Findings

Explicit descriptions for rank 2 and 3 $(k,l)$-stable bundles.

Relations established between $(k,l)$-stability and Brill-Noether loci.

Insights into the connection between stability notions and Segre invariants.

Abstract

In this paper, we study the $(k,l)$-stable vector bundles over non-singular projective curve $X$ of genus $g\geq 2,$ its relation with stability and Segre invariants. For rank 2 and 3, we give an explicit description and relation of $(k,l)$-stability and Brill-Noether loci.