Graded derivation modules and algebraic free divisors
type: Item
instance of: scholarly article
title: Graded derivation modules and algebraic free divisors
zbMATH Open document ID: 1327.13096
author: Cleto B. Miranda-Neto
published in: Journal of Pure and Applied Algebra
publication date: 2015-08-31T00:00:00Z
review text: The main goal of the article is to provide new characterizations of what it means for certain homogeneous forms to be free divisors (in the sense of [\textit{K. Saito}, J. Fac. Sci., Univ. Tokyo, Sect. I A 27, 265--291 (1980; Zbl 0496.32007)]). These characterizations are given in terms of the minimal number of generators of particular modules of derivations associated to the hypersurface ring defined by the form. Along the way, the author investigates several invariants of the modules of derivations of such hypersurface rings, such as the Castelnuovo-Mumford regularity and the Hilbert function. The case of a cuspidal projective plane cubic is examined in detail. A characterization of \(linear\) free divisors, as defined in [\textit{R.-O. Buchweitz} and \textit{D. Mond}, Lond. Math. Soc. Lect. Note Ser. 324, 41--77 (2006; Zbl 1101.14013)], involving the Ulrichness of a certain ideal, is also established.
Mathematics Subject Classification ID: 13N15
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 37F75
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 6476977
zbMATH Keywords: derivations
zbMATH Keywords: free divisors
zbMATH Keywords: hypersurfaces
zbMATH Keywords: Castelnuovo-Mumford regularity
zbMATH Keywords: Hilbert function
zbMATH Keywords: Ulrich modules
reviewed by: Michael Brown
describes a project that uses: Macaulay2
MaRDI profile type: Publication
full work available at URL: j.jpaa.2015.05.026
OpenAlex ID: W2202029609
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DOI: 10.1016/J.JPAA.2015.05.026
description: scientific article; zbMATH DE number 6476977