Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces

2017/05/23 by Coskun, Izzet, Huizenga, Jack · 1 citation
#14D20 #14F05 (Secondary) #14J26 (Primary) #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.08460

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.

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