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arXiv · 1705.08460

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

Izzet Coskun·Jack Huizenga
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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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Izzet Coskun, Jack Huizenga. 2017-05-23. Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces. https://arxiv.org/abs/1705.08460

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