Ample stable vector bundles on rational surfaces

Abstract

We study ample stable vector bundles on minimal rational surfaces. We give a complete classification of those moduli spaces for which the general stable bundle is both ample and globally generated. We also prove that if V is any stable bundle, then a large enough direct sum $V^{\oplus n}$ has ample deformations unless there is an obvious numerical reason why it cannot. Previous work in this area has mostly focused on rank two bundles and relied primarily on classical sconstructions such as the Serre construction. In contrast, we use recent advances in moduli of vector bundles to obtain strong results for vector bundles of any rank.

Keywords:

• Ample vector bundles
• moduli spaces of sheaves

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 14J60
• 14J26
• Secondary: 14D20

Acknowledgments

We would like to thank Izzet Coskun for many valuable discussions.

Additional information

Funding

During the preparation of this article the first author was partially supported by the NSF FRG grant DMS 1664303.