Buchsbaum-Rim sheaves and their multiple sections
| dc.creator | Migliore, J. C. | |
| dc.creator | Nagel, U. | |
| dc.creator | Peterson, C. | |
| dc.date | 1997-08-26 | |
| dc.date.accessioned | 2026-07-07T09:07:23Z | |
| dc.date.available | 2026-07-07T09:07:23Z | |
| dc.description | 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 $ψ: \cP \to \cBf$ of sheaves on $Z$ dropping rank in the expected codimension, where $H^0_*(Z,\cP)$ 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. | |
| dc.description | 27 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9708022 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9708022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150353 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Primary 14F05; Secondary 13D02, 13D45 | |
| dc.title | Buchsbaum-Rim sheaves and their multiple sections | |
| dc.type | text |