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Differential equations on complex projective hypersurfaces of low dimension
- Part of
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- Journal:
- Compositio Mathematica / Volume 144 / Issue 4 / July 2008
- Published online by Cambridge University Press:
- 01 July 2008, pp. 920-932
- Print publication:
- July 2008
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- Article
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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 .
. In this paper we find an effective lower bound for the degree of 