On full exceptional collections of line bundles on del Pezzo surfaces
Algebraic Geometry
2017-10-10 v3
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.
Keywords
Cite
@article{arxiv.1505.06477,
title = {On full exceptional collections of line bundles on del Pezzo surfaces},
author = {Alexey Elagin and Valery Lunts},
journal= {arXiv preprint arXiv:1505.06477},
year = {2017}
}
Comments
20 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)