Differential equations on hypersurfaces in \(\mathbb P^4\).
type: Item
instance of: scholarly article
title: Differential equations on hypersurfaces in \(\mathbb P^4\).
zbMATH Open document ID: 1115.14009
author: Erwan Rousseau
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2007-02-13T00:00:00Z
review text: Here the author proves that for all integers \(d \geq 97\) (resp. \(d \geq 92\)) and every smooth degree \(d\) hypersurface \(X \subset \mathbb {P}^4_{\mathbb {C}}\) every entire curve of \(X\) (resp. \(\mathbb {P}^4_{\mathbb {C}}\backslash X\)) satisfies an algebraic differential equation of degree \(3\). The main tool is the logarithmic version of Demailly vector bundle of differential jets [\textit{G. Dethloff} and \textit{S. Lu}, Osaka J. Math. 38, No. 1, 185--237 (2001; Zbl 0982.32022)]. Apart from this fundamental tool the main trick is to use the decomposition of the graded object obtained from the vector bundle of jets of order \(3\) into Schur's irreducible representations.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 32Q45
zbMATH DE Number: 5125005
zbMATH Keywords: Kobayashi hyperbolicity
zbMATH Keywords: Schur representations
zbMATH Keywords: smooth hypersurface
zbMATH Keywords: logarithmic jets
zbMATH Keywords: algebraic differential equation
zbMATH Keywords: entire curve
MaRDI profile type: Publication
full work available at URL: j.matpur.2006.06.004
OpenAlex ID: W2218014137
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DOI: 10.1016/J.MATPUR.2006.06.004
description: scientific article; zbMATH DE number 5125005