Factorization of birational morphisms with fiber dimension bounded by 1
type: Item
instance of: scholarly article
title: Factorization of birational morphisms with fiber dimension bounded by 1
zbMATH Open document ID: 0672.14003
DOI: 10.1007/BF01462880
author: Tie Luo
author: Zhaohua Luo
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164478
review text: In this note the authors give, both in the local and in the global case, an algebraic proof of the following statement: Let \(f: X\to Y\) be a projective birational morphism of regular noetherian integral schemes with fibres of dimension \(\leq 1\), then f is a composition of blow-ups with non singular centres of codimension 2. This result, which includes the Zariski theorem for birational morphisms of smooth algebraic surfaces, extends to schemes a similar result for smooth algebraic varieties proved by \textit{V. I. Danilov} [Math. USSR, Izv. 16, 419-429 (1981); translation of Izv. Akad. Nauk SSSR, Ser. Mat. 44, 465-477 (1980; Zbl 0453.14004)].
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14B25
zbMATH DE Number: 4099457
zbMATH Keywords: factorization of birational morphisms
reviewed by: Luciana Picco Botta
MaRDI profile type: Publication
cites work: Q3900168
cites work: Q4212433
description: scientific article; zbMATH DE number 4099457