Recollements and Ladders for weighted projective lines

Abstract

In this paper, we construct recollements and ladders for exceptional curves by using reduction/insertion functors due to $p$-cycle construction. As applications to weighted projective lines, we classify recollements for the category of coherent sheaves over a weighted projective line, and give an explicit description of ladders in two different levels: the bounded derived category of coherent sheaves and the stable category of vector bundles.