a1 Institut Fourier, Université de Grenoble I, BP 74, F-38402, Saint Martin d’Héres, France (email: email@example.com)
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 .
(Received July 23 2007)
(Accepted November 26 2007)
2000 Mathematics subject classification
p1 Current address: Istituto ‘Guido Castelnuovo’, Università di Roma ‘La Sapienza’, P. le Aldo Moro 2, 00185 Roma, Italy