Torsion exceptional sheaves on weak del Pezzo surfaces of Type A
  We investigate torsion exceptional sheaves on a weak del Pezzo surface of degree greater than two whose anticanonical model has at most $A_n$-singularities. We show that every torsion exceptional sheaf can be obtained from a line bundle on a $(-1)$-curve by acting spherical twist functors successively. 
Pu Cao, Chen Jiang
math.AG