Algebraic hyperbolicity of generic high degree hypersurfaces
type: Item
instance of: scholarly article
title: Algebraic hyperbolicity of generic high degree hypersurfaces
zbMATH Open document ID: 0803.14023
DOI: 10.1007/BF01189831
author: E. Ballico
published in: Archiv der Mathematik
publication date: 1994-11-13T00:00:00Z
review text: Here we show (in any characteristic) that for every \(n \geq 3\) there is an explicit integer \(d(n)\) such that for every \(d \geq d(n)\) a generic (i.e. outside countably many proper subvarieties of the parameter space) hypersurface \(S\) of degree \(d\) of \(\mathbb{P}^ n\) is algebraically hyperbolic, i.e. it contains no image of an abelian variety (hence no rational or elliptic curve (even singular)). Recently over \(\mathbb{C}\) a much stronger result (the hyperbolicity of \(S)\) was independently proved by \textit{K. Masuda} and \textit{J. Noguchi} [``A construction of hyperbolic hypersurface of \(\mathbb{P}^ n (\mathbb{C})\)''].
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14K99
zbMATH DE Number: 687047
zbMATH Keywords: algebraically hyperbolic hypersurface
MaRDI profile type: Publication
cites work: Curves on generic hypersurfaces
cites work: Q4023939
cites work: Subvarieties of general hypersurfaces in projective space
full work available at URL: https://doi.org/10.1007/bf01189831
OpenAlex ID: W2035079120
description: scientific article; zbMATH DE number 687047