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Differential equations on complex projective hypersurfaces of low dimension

Published online by Cambridge University Press:  01 July 2008

Simone Diverio*
Affiliation:
Institut Fourier, Université de Grenoble I, BP 74, F-38402, Saint Martin d’Héres, France (email: sdiverio@fourier.ujf-grenoble.fr)
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Abstract

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Let n=2,3,4,5 and let X be a smooth complex projective hypersurface of . In this paper we find an effective lower bound for the degree of X, such that every holomorphic entire curve in X must satisfy an algebraic differential equation of order k=n=dim X, and also similar bounds for order k>n. Moreover, for every integer n≥2, we show that there are no such algebraic differential equations of order k<n for a smooth hypersurface in .

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2008