BRILL-NOETHER THEOREMS and GLOBALLY GENERATED VECTOR BUNDLES on HIRZEBRUCH SURFACES

Izzet Coskun, Jack Huizenga

Research output: Contribution to journalArticle

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1-36
Number of pages36
JournalNagoya Mathematical Journal
Volume238
DOIs
StatePublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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