On exceptional collections of line bundles on weak del Pezzo surfaces

Autor:	Elagin, Alexey, Xu, Junyan, Zhang, Shizhuo
Rok vydání:	2017
Předmět:	Mathematics - Algebraic Geometry 14F05 14J26
Druh dokumentu:	Working Paper
Popis:	We study full exceptional collections of line bundles on surfaces. We prove that any full strong exceptional collection of line bundles on a weak del Pezzo surface of degree $\ge 3$ is an augmentation in the sense of L.Hille and M.Perling, while for some weak del Pezzo surfaces of degree $2$ the above is not true. We classify smooth projective surfaces possessing a cyclic strong exceptional collection of line bundles of maximal length: we prove that they are weak del Pezzo surfaces and find all types of weak del Pezzo surfaces admitting such a collection. We find simple criteria of exceptionality/strong exceptionality for collections of line bundles on weak del Pezzo surfaces. Comment: 61 pages, files with computer programs are attached. Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1710.03972 Zobrazit plný text záznamu View this record from Arxiv