Tilting bundles for weighted projective lines of weight type $(p,q)$

Abstract

. We give a combinatorial description of tilting bundles in the category of coherent sheaves over the weighted projective line of type ( p, q ) . We define a set of admissible paths in the rectangular area D ( p,q ) = [1 , p − 1] × [1 , q − 1] , and show that there is a bijection between the fundamental tilting bundles and the admissible paths in D ( p,q ) .