On full exceptional collections of line bundles on del Pezzo surfaces

Abstract

We prove that any numerically exceptional collection of maximal length, consisting of line bundles, on a smooth del Pezzo surface is a standard augmentation in the sense of L.Hille and M.Perling. We deduce that any such collection is exceptional and full.

arXiv comment20 pages. v2: major changes. More simple proof of the main theorem is given. Consideration of toric vectors and three-block collections is not needed now hence omitted. v3: some generalizations are made. Main theorem is proved now for numerically exceptional collections (rather than strong exceptional collections)