A recollement of vector bundles

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 $r^{\prime }$ with $r^{\prime }\le r$, 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 $(p,q,r^{\prime })$ and $(p,q,r-r^{\prime }+1)$.