Differential Equations on Complex Projective Hypersurfaces of Low Dimension

Details Differential Equations on Complex Projective Hypersurfaces of Low Dimension Differential Equations on Complex Projective Hypersurfaces of Low Dimension

2007-06-07

arxiv.org/abs/0706.1031v3

Mathematics

Algebraic Geometry

Final version, some minor changes according to referee's suggestions, to appear in Compositio Mathematica

Scientific paper

Let $n=2,3,4,5$ and let $X$ be a smooth complex projective hypersurface of $\mathbb P^{n+1}$. 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 $n\ge 2$, we show that there are no such algebraic differential equations of order $k

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