1997/08/26 by Migliore, J. C., Nagel, U., Peterson, C.
#13D45 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 14F05 #Secondary 13D02
paper · doi:10.48550/arxiv.alg-geom/9708022
This paper begins by introducing and characterizing Buchsbaum-Rim sheaves on Z = \Proj R where R is a graded Gorenstein K-algebra. They are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between free R-modules. Then we study multiple sections of a Buchsbaum-Rim sheaf \cBf, i.e, we consider morphisms ψ: \cP → \cBf of sheaves on Z dropping rank in the expected codimension, where H0_*(Z,\cP) is a free R-module. The main purpose of this paper is to study properties of schemes associated to the degeneracy locus S of ψ. 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 modules and describe ring-theoretic properties of their coordinate rings. Moreover, we produce graded free resolutions of X (and S) which are in general minimal. Among the applications we show how one can embed a subscheme 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 arithmetically Buchsbaum.