BuchsbaumRim sheaves and their multiple sections
Abstract
This paper begins by introducing and characterizing BuchsbaumRim sheaves on $Z = \Proj R$ where $R$ is a graded Gorenstein Kalgebra. They are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between free Rmodules. Then we study multiple sections of a BuchsbaumRim sheaf $\cBf$, i.e, we consider morphisms $\psi: \cP \to \cBf$ of sheaves on $Z$ dropping rank in the expected codimension, where $H^0_*(Z,\cP)$ is a free Rmodule. The main purpose of this paper is to study properties of schemes associated to the degeneracy locus $S$ of $\psi$. It turns out that $S$ is often not equidimensional. Let $X$ denote the topdimensional part of $S$. In this paper we measure the ``difference'' between $X$ and $S$, compute their cohomology modules and describe ringtheoretic 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 zeroloci of sections of the dual of a null correlation bundle are arithmetically Buchsbaum.
 Publication:

arXiv eprints
 Pub Date:
 August 1997
 DOI:
 10.48550/arXiv.alggeom/9708022
 arXiv:
 arXiv:alggeom/9708022
 Bibcode:
 1997alg.geom..8022M
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra;
 Primary 14F05;
 Secondary 13D02;
 13D45
 EPrint:
 27 pages, AMSLaTeX