Varieties with non-linear Gauss fibers
type: Item
instance of: scholarly article
title: Varieties with non-linear Gauss fibers
zbMATH Open document ID: 1093.14073
author: Satoru Fukasawa
published in: Mathematische Annalen
publication date: 2006-03-21T00:00:00Z
full work available at URL: http://ir.lib.hiroshima-u.ac.jp/00017229
review text: Let \(X \subset \mathbb P^n\) be an integral variety. In characteristic zero the general fiber of the Gauss map \(\gamma _X\) of \(X\) is a linear space, but in positive characteristic this is in general false [see \textit{A. Noma}, J. Pure Appl. Algebra 156, No. 1, 81--93 (2001; Zbl 0974.14037) and references therein]. In the paper under review for any positive characteristic algebraically closed field and for all integers \(k \geq 2\), \(0 \leq r \leq k\) and \(n \geq r+k\) and any integral \(r\)-codimensional projective variety \(Y \subseteq \mathbb P^r\) the author constructs a \(k\)-dimensional projective variety \(X \subset \mathbb P^n\) such that \(Y\) is (set-theoretically) a general fiber of \(\gamma _X\).
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 5013660
zbMATH Keywords: Gauss map
zbMATH Keywords: separable degree
zbMATH Keywords: Gauss mapping
zbMATH Keywords: generic fiber
MaRDI profile type: Publication
OpenAlex ID: W2076381717
cites work: Developable varieties in positive characteristic
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cites work: Q3033882
cites work: Gauss maps with nontrivial separable degree in positive characteristic
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cites work: Q3140224
DOI: 10.1007/S00208-005-0688-5
description: scientific article; zbMATH DE number 5013660