Bertini- type theorems in positive characteristic
type: Item
instance of: scholarly article
title: Bertini- type theorems in positive characteristic
zbMATH Open document ID: 0820.14004
DOI: 10.1007/BF01188571
author: Bin Zhang
published in: Archiv der Mathematik
publication date: 1995-09-17T00:00:00Z
review text: Let \(k\) be an algebraically closed field, \(X\) be a scheme of finite type over the projective space of dimension \(n\) over \(k\). We prove that if \(X\) is geometrically unibranch, a general hyperplane section of \(X\) is geometrically unibranch. We also prove that if \(X\) satisfies some technical condition \((R)\) (resp. \((N))\), then a general hyperplane section of \(X\) is smooth on \(k\) (resp. normal) if \(X\) is smooth on \(k\) (resp. normal). If \(k\) is of characteristic zero or if \(X\) is unramified over the projective space, then the condition \((R)\) (resp. \((N))\) holds automatically.
Mathematics Subject Classification ID: 14B99
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14C17
zbMATH DE Number: 756420
zbMATH Keywords: positive characteristic
zbMATH Keywords: general hyperplane section
zbMATH Keywords: geometrically unibranch section
MaRDI profile type: Publication
cites work: Q4749947
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cites work: Q4775956
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description: scientific article; zbMATH DE number 756420