On equimultiple subschemes of a local scheme over a field of characteristic zero
type: Item
instance of: scholarly article
title: On equimultiple subschemes of a local scheme over a field of characteristic zero
zbMATH Open document ID: 0601.14006
author: Dieter Nesselmann
published in: Beiträge zur Algebra und Geometrie
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138326
review text: Let X be the spectrum of a quasi-unmixed local Nagata ring over a field of characteristic zero, and let Y be a reduced closed subscheme of X. The main result of the paper is the following: if x is the closed point of X and if X is equimultiple along Y, then the embedding dimension of Y at x is less than or equal to dim(X). Then the author applies this result to get a stability theorem for standard bases and a structure theorem for tangent cones.
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 14A05
zbMATH DE Number: 3968746
zbMATH Keywords: multiplicity
zbMATH Keywords: spectrum of a quasi-unmixed local Nagata ring
zbMATH Keywords: embedding dimension
zbMATH Keywords: standard bases
zbMATH Keywords: tangent cones
reviewed by: Lucian Bădescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3968746