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Differential equations on complex projective hypersurfaces of low dimension

Part of: (Co)homology theory Complex manifolds

Published online by Cambridge University Press:  01 July 2008

Simone Diverio
Simone Diverio*
Affiliation:
Institut Fourier, Université de Grenoble I, BP 74, F-38402, Saint Martin d’Héres, France (email: [email protected])
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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 .

Keywords

Kobayashi hyperbolicityinvariant jet differentialsSchur powersholomorphic Morse inequalities

MSC classification

Secondary: 14F99: None of the above, but in this section 32Q45: Hyperbolic and Kobayashi hyperbolic manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 4 , July 2008 , pp. 920 - 932
Copyright
Copyright © Foundation Compositio Mathematica 2008