Buchsbaum-Rim sheaves and their multiple sections

Juan C. Migliore, Uwe Nagel, Chris Peterson

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This paper begins by introducing and characterizing Buchsbaum-Rim sheaves on Z=ProjR, 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 Bφ, i.e, we consider morphisms ψ: P→Bφ of sheaves on Z dropping rank in the expected codimension, where H0*(Z,P) 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.

Original languageEnglish
Pages (from-to)378-420
Number of pages43
JournalJournal of Algebra
Issue number1
StatePublished - Sep 1 1999


  • Arithmetically Buchsbaum scheme
  • Arithmetically Cohen-Macaulay
  • Arithmetically Gorenstein
  • Bott formula
  • Buchsbaum-Rim complex
  • Buchsbaum-Rim sheaf
  • Degeneracy locus
  • Eagon-Northcott complex
  • Minimal free resolution
  • k-Buchsbaum sheaves

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Buchsbaum-Rim sheaves and their multiple sections'. Together they form a unique fingerprint.

Cite this