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ISRN Algebra
Volume 2011 (2011), Article ID 659672, 12 pages
http://dx.doi.org/10.5402/2011/659672
Research Article

Examples of Stability of Tensor Products in Positive Characteristic

Universidad Autónoma, “Benito Juárez” de Oaxaca, Mexico

Received 5 June 2011; Accepted 3 July 2011

Academic Editor: V. Futorny

Copyright © 2011 A. S. Argáez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let X be projective smooth variety over an algebraically closed field k and let , be μ-semistable locally free sheaves on X. When the base field is , using transcendental methods, one can prove that the tensor product is always a μ-semistable sheaf. However, this theorem is no longer true over positive characteristic; for an analogous theorem one needs the hypothesis of strong μ-semistability; nevertheless, this hypothesis is not a necessary condition. The objective of this paper is to construct, without the strongly μ-semistability hypothesis, a family of locally free sheaves with μ-stable tensor product.