On curvilinear subschemes of \(\mathbb{P}^ 2\)
type: Item
instance of: scholarly article
title: On curvilinear subschemes of \(\mathbb{P}^ 2\)
zbMATH Open document ID: 0803.14001
DOI: 10.1016/0022-4049(94)90077-9
author: Alessandro Gimigliano
author: Maria Virginia Catalisano
published in: Journal of Pure and Applied Algebra
publication date: 1994-12-15T00:00:00Z
review text: Let \(Z\) be a curvilinear subscheme of \(\mathbb{P}^ 2\), i.e. a 0-dimensional scheme whose embedding dimension at every point of is support is \(\leq 1\). The relevance of such schemes lies in at least two facts: (a) they are the only non-reduced 0-dimensional schemes which lie on nonsingular plane curves i.e. they can be viewed as divisors on some smooth plane curve; (b) the generic non-reduced 0-dimensional subscheme of \(\mathbb{P}^ 2\) is curvilinear. The authors find a bound for the minimum degree of the plane curves on which \(Z\) imposes independent conditions and show that the Hilbert function of \(Z\) is maximal for a ``generic choice'' of \(Z\). They work over an algebraically closed field.
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 561568
zbMATH Keywords: curvilinear subscheme
zbMATH Keywords: divisors
zbMATH Keywords: Hilbert function
reviewed by: A. Del Centina
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90077-9
OpenAlex ID: W2019085743
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description: scientific article; zbMATH DE number 561568