On the stability of kernel bundles over chain-like curves

TL;DR

This paper investigates the stability properties of kernel bundles over chain-like curves, providing insights into their behavior in algebraic geometry and vector bundle theory.

Contribution

It introduces new criteria for the (semi)stability of kernel bundles on chain-like curves, extending previous understanding in the field.

Findings

Established conditions for stability and semistability of kernel bundles

Analyzed the influence of the curve's chain structure on bundle stability

Provided examples illustrating the stability criteria

Abstract

Let $C$ be a chain-like curve having $n$ smooth components and $n-1$ nodes, where $n \geq 2$. Let $E$ be a vector bundle on $C$ and $V \subseteq H^0(E)$ be a linear subspace generating $E$. We investigate the (semi)stability of the kernel bundle $M_{E,V}$ associated to $(E,V)$.