Examples of Stability of Tensor Products in Positive Characteristic. (19th September 2011)

• Record Type: Journal Article
• Authors: Argáez, A. S.
• Other Names: Futorny V. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2011(2011)
• Publication Date: 2011-09-19
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.5402/2011/659672
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : Let X be projective smooth variety over an algebraically closed field k and let ℰ, ℱ be μ -semistable locally free sheaves on X. When the base field is ℂ, using transcendental methods, one can prove that the tensor productℰ ⊗ ℱ 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.