Examples of Stability of Tensor Products in Positive Characteristic. (19th September 2011) - Argáez, A. S.
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.