Exceptional Vector Bundles on a Del Pezzo Surface

Abstract

An exceptional bundle is basically a bundle whose analytical or algebraic structure is uniquely determined by its topological one. This phenomenon was discovered in the mid eighties while studying vector bundles over complex algebraic surfaces or real 4-manifolds. Since then there were several attempts to investigate exceptional vector bundles and to use them in vector bundle theory and in the classification of 4-manifolds. Main idea of this article is to combine results and conjectures for bundles on a Del Pezzo surface. The author feels strongly that the context of Del Pezzo surfaces has several advantages and understanding here could develop really rapidly. Our aim is to influence such a development.