Subschemes of special determinantal and Pfaffian projective schemes
type: Item
instance of: scholarly article
title: Subschemes of special determinantal and Pfaffian projective schemes
zbMATH Open document ID: 1179.13017
author: Alfio Ragusa
author: Giuseppe Zappalà
published in: Results in Mathematics
publication date: 2009-11-09T00:00:00Z
review text: By the well-known result of Hilbert-Burch resp. Buchsbaum-Eisenbud an arithmetically Cohen-Macaulay codimension 2 resp. an arithmetically Gorenstein codimension 3 subscheme is defined by the maximal minors of an \(r \times (r+1)\)-matrix resp. by the submaximal Pfaffians of a skew-symmetric matrix. In the paper under review the authors consider particular cases of these kind of varieties where the corresponding matrices have ``too many'' zeros on the lower right part. The precise definition in the paper is called \(Z_{\rho}\)-type property. It turns out that this special form of the structure matrices forces the schemes to have two ``natural'' subschemes completely determined by the matrix. As applications of their technique the authors recover a result of \textit{E. D. Davis} [Rend. Sem. Mat., Torino 42, No. 2, 25--28 (1984; Zbl 0598.14047)], and some of their own [Commun. Algebra 29, No. 1, 303--318 (2001; Zbl 1027.14022)].
reviewed by: Peter Schenzel
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 5627207
zbMATH Keywords: codimension 2 arithmetically Cohen-Macaulay subscheme
zbMATH Keywords: codimension 3 arithmetically Gorenstein subscheme
MaRDI profile type: Publication
full work available at URL: s00025-009-0392-y
OpenAlex ID: W2025502399
DOI: 10.1007/S00025-009-0392-Y
description: scientific article; zbMATH DE number 5627207