Linear and Steiner Bundles on Projective Varieties

Abstract

We generalize the theory of Horrocks monads to ACM varieties, and use the generalization to establish a cohomological characterization of linear and Steiner bundles on projective space and on quadric hypersurfaces. We also characterize Steiner bundles on the Grassmannian G(1, 4) of lines in ℙ⁴. Finally, we study linear resolutions of bundles on ACM varieties, and characterize linear homological dimension on quadric hypersurfaces.

Key Words:

• Linear bundles
• Monads
• Steiner bundles

2000 Mathematics Subject Classification:

• 14J60

ACKNOWLEDGMENTS

We thank N. Mohan Kumar and Rosa Maria Miró-Roig for answering of our questions regarding their work. We also thank Steven Kleiman for his many comments and his help in improving this article. The first named author is partially supported by the CNPq grant number 305464/2007-8 and the FAPESP grant number 2005/04558-0. The second named author is partially supported by CNPq grant number PDE 200999/2005-2.

Notes

Communicated by S. Kleiman.