## Abstract

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 B_{φ}, i.e, we consider morphisms ψ: P→B_{φ} 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 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 language | English |
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Pages (from-to) | 378-420 |

Number of pages | 43 |

Journal | Journal of Algebra |

Volume | 219 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 1999 |

## Keywords

- 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