A recollement of vector bundles

TL;DR

This paper establishes an explicit recollement structure for the stable category of vector bundles on weighted projective lines, relating categories with different weights through a triangulated framework.

Contribution

It introduces a new recollement construction that connects stable categories of vector bundles across weighted projective lines with varying weights.

Findings

Recollement structure explicitly constructed for weighted projective lines.

Triangulated category framework applied to vector bundles.

Connections established between categories with different weights.

Abstract

For a weighted projective line, the stable category of its vector bundles modulo lines bundles has a natural triangulated structure. We prove that, for any positive integers $p, q, r$ and $r'$ with $r'\leq r$, there is an explicit recollement of the stable category of vector bundles on a weighted projective line of weight type $(p, q, r)$ relative to the ones on weighted projective lines of weight types $(p, q, r')$ and $(p, q, r-r'+1)$.