On the length of the absolute Samuel stratum
type: Item
instance of: scholarly article
title: On the length of the absolute Samuel stratum
zbMATH Open document ID: 0707.14009
DOI: 10.1016/0021-8693(90)90028-M
author: Juan B. Sancho de Salas
author: Juan A. Navarro González
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let X be a scheme of finite type over \({\mathbb{C}}\). The following result is proved: Let x be a generic point of the center of a permissible monoidal transformation \(X'\to X\) and let y be any generic point of \(\Pr oj(T_ xX)\). If \(s_{X,x}\) is finite, then \(s_{X',y}<s_{X,x}\) or \(H^{(r)}_{X',y}<H_{X,x}\). - Here r is the transcendence degree of \({\mathbb{C}}(y)\) over \({\mathbb{C}}(x)\), \(s_{X,x}\) is the length of the Samuel stratum of X passing through x and \(H_{X,x}\) is the Hilbert-Samuel function. The technique of the proof has applications to the theory of maximal contact.
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 4160912
zbMATH Keywords: monoidal transformation
zbMATH Keywords: length of the Samuel stratum
zbMATH Keywords: Hilbert-Samuel function
zbMATH Keywords: maximal contact
reviewed by: Nicolae Mihalache
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4160912