Exceptional bundles on surfaces with a moving anticanonical class

The author studies the properties of exceptional coherent sheaves on algebraic surfaces $S$ with $\operatorname{dim}H^0(-\mathscr K_S)\geqslant2$ and describes a method for constructing infinite families of such sheaves, based on the technique developed here of reconstructions of the exceptional objects of a derived category.
Bibliography: 12 titles.