2017/10/11 by Elagin Alexey, Elagin, Alexey, Junyan Xu +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1710.03972
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 ≥ 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.