Lifting the \(k\)-Buchsbaum property
type: Item
instance of: scholarly article
title: Lifting the \(k\)-Buchsbaum property
zbMATH Open document ID: 0968.14027
DOI: 10.1016/S0022-4049(99)00130-9
author: Uwe Nagel
published in: Journal of Pure and Applied Algebra
publication date: 2001-09-23T00:00:00Z
review text: Let \(X\subset\mathbb{P}^n\) be an equidimensional projective subscheme and \(F\) be a sufficiently general hypersurface of \(\mathbb{P}^n\). \(X\) is said to be \(k\)-Buchsbaum if \[ (x_0,x_1, \dots,x_n)^k \cdot\bigoplus_{t\in \mathbb{Z}}H^i\bigl( \mathbb{P}^n, {\mathcal I}_X(t) \bigr)=0 \] where \(K[x_0,x_1, \dots,x_n]\) is the coordinate ring of \(\mathbb{P}^n\) and \({\mathcal I}_X\) is the sheaf ideal of \(X\). In this paper the author considers relation between the \(k\)-Buchsbaum property for \(X\) and for \(F\cap X\). He also investigates consequences of \(k\)-Buchsbaum on the degree of \(F\).
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 14B15
zbMATH DE Number: 1517306
zbMATH Keywords: Buchsbaum hypersurface
reviewed by: Marcel Morales
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1517306