Buchsbaum-Rim sheaves and their multiple sections

This paper begins by introducing and characterizing Buchsbaum-Rim sheaves o n Z = Proj R, where R is a graded Gorenstein K-algebra, They are reflexive sheaves arising as the sheafification of kernels of sufficiently general ma ps between free R-modules. Then we study multiple sections of a Buchsbaum-R im sheaf B-phi, i.e, we consider morphisms psi: P --> B-phi, of sheaves on Z dropping rank in the expected codimension, where H*(0)(Z, P) is a free R- module. The main purpose of this paper is to study properties of schemes as sociated to the degeneracy locus S of psi. It turns out that S is often not equidimensional. Let X denote the top-dimensional part of S. In this paper we measure the "difference" between X and S, compute their cohomology modu les and describe ring-theoretic properties of their coordinate rings. Moreo ver, we produce graded free resolutions of X (and S) which are in general m inimal. Among the applications we show how one can embed a sub-scheme into an arithmetically Gorenstein subscheme of the same dimension and prove that zero-loci of sections of the dual of a null correlation bundle are arithme tically Buchsbaum. (C) 1999 Academic Press.