학술논문
Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces
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Working Paper
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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.
Comment: v2: Minor corrections. Results in section 5 extended to the rank 1 case
Comment: v2: Minor corrections. Results in section 5 extended to the rank 1 case