On cyclic strong exceptional collections of line bundles on surfaces
Abstract
We study exceptional collections of line bundles on surfaces. We prove that any full cyclic strong exceptional collection of line bundles on a rational surface is an augmentation in the sense of L.Hille and M.Perling. We find simple geometric criteria of exceptionality (strong exceptionality, cyclic strong exceptionality) for collections of line bundles on weak del Pezzo surfaces. As a result, we classify smooth projective surfaces admitting a full cyclic strong exceptional collection of line bundles. Also, we provide an example of a weak del Pezzo surface of degree 2 and a full strong exceptional collection of line bundles on it which does not come from augmentations, thus answering a question by Hille and Perling.
Keywords
Cite
@article{arxiv.2007.02140,
title = {On cyclic strong exceptional collections of line bundles on surfaces},
author = {Alexey Elagin and Junyan Xu and Shizhuo Zhang},
journal= {arXiv preprint arXiv:2007.02140},
year = {2020}
}
Comments
This is a seriously rewritten part of the paper arXiv.math:1710.03972, accepted to EJM. Here we concentrate on the cyclic strong exceptional collections. 35 pages