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 $r'$ 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 $(p, q, r-r'+1)$.