$(t,\ell)$-stability and coherent systems

TL;DR

This paper introduces $(t,\ell)$-stability to demonstrate the existence of certain $\\alpha$-stable coherent systems on complex algebraic curves of genus at least 2, regardless of the stability parameter.

Contribution

It establishes the existence of $\\alpha$-stable coherent systems using $(t,\ell)$-stability, a novel approach in the context of algebraic curves.

Findings

Existence of $\\alpha$-stable coherent systems for all positive $\\alpha$

Application of $(t,\ell)$-stability to stability problems

Results hold for curves of genus $g \geq 2$

Abstract

Let $X$ be a non-singular irreducible complex projective curve of genus $g\geq 2$. We use $(t,\ell)$-stability to prove the existence of coherent systems over $X$ that are $\alpha$-stable for all allowed $\alpha >0$.