Smooth projective varieties dominated by smooth quadric hypersurfaces in any characteristic
type: Item
instance of: scholarly article
title: Smooth projective varieties dominated by smooth quadric hypersurfaces in any characteristic
zbMATH Open document ID: 0815.14035
DOI: 10.1007/BF02571960
author: Koji Cho
author: Ei-ichi Sato
published in: Mathematische Zeitschrift
publication date: 1995-07-02T00:00:00Z
full work available at URL: https://eudml.org/doc/174706
review text: We consider the following problem due to Remmert, Van de Ven and Lazarsfeld: Let \(X\) be a smooth projective variety defined over the complex number field \(\mathbb{C}\). Let \(f : G/P \to X\) be a surjective morphism where \(G\) is a simple classical group and \(P\) a maximal parabolic subgroup of \(G\). Then unless \(f\) is an isomorphism, \(X\) is isomorphic to a projective space. -- Here we show: Main theorem: Let \(X\) be a smooth projective variety, \(Q\) a smooth quadric hypersurface of dimension \(\geq 3\) and \(f\) a surjective morphism defined over an algebraically closed field of any characteristic (char \(k \neq 2)\). Assume that \(f\) is separable. Then unless \(f\) is an isomorphism, \(X\) is isomorphic to a projective space.
Mathematics Subject Classification ID: 14P05
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 14E99
zbMATH DE Number: 737153
zbMATH Keywords: quadric hypersurface dominating a variety
zbMATH Keywords: characterisation of projective space
MaRDI profile type: Publication
cites work: Projective manifolds with ample tangent bundles
cites work: Self maps of homogeneous spaces
cites work: Über holomorphe Abbildungen projektiv-algebraischer Mannigfaltigkeiten auf komplexe Räume
OpenAlex ID: W1995179161
description: scientific article; zbMATH DE number 737153