Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces
Algebraic Geometry
2018-05-17 v2
Abstract
In this paper, we show that the cohomology of a general stable bundle on a Hirzebruch surface is determined by the Euler characteristic provided that the first Chern class satisfies necessary intersection conditions. More generally, we compute the Betti numbers of a general stable bundle. We also show that a general stable bundle on a Hirzebruch surface has a special resolution generalizing the Gaeta resolution on the projective plane. As a consequence of these results, we classify Chern characters such that the general stable bundle is globally generated.
Cite
@article{arxiv.1705.08460,
title = {Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces},
author = {Izzet Coskun and Jack Huizenga},
journal= {arXiv preprint arXiv:1705.08460},
year = {2018}
}
Comments
v2: Minor corrections. Results in section 5 extended to the rank 1 case