Cohomological characterisation of Steiner bundles

Abstract

A vector bundle E on a smooth irreducible algebraic variety X is called a Steiner bundle of type ( F 0 , F 1 ) if it is defined by an exact sequence of the form where s, t ≥ 1 and ( F 0 , F 1 ) is a strongly exceptional pair of vector bundles on X such that is generated by global sections. Let X be a smooth irreducible projective variety of dimension n with an n -block collection , of locally free sheaves on X which generate D b (𝒪 X – mod ). We give a cohomological characterisation of Steiner bundles of type on X , where 0 ≤ a < b ≤ n and 1 ≤ i 0 ≤ α a , 1 ≤ j 0 ≤ α b .