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Title: BRILL–NOETHER THEOREMS AND GLOBALLY GENERATED VECTOR BUNDLES ON HIRZEBRUCH SURFACES
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.  more » « less
Award ID(s):
1664303
PAR ID:
10065476
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Nagoya Mathematical Journal
ISSN:
0027-7630
Page Range / eLocation ID:
1 to 36
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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