Nondeformability of entire curves in projective hypersurfaces of high degree

Details Nondeformability of entire curves in projective hypersurfaces of high degree Nondeformability of entire curves in projective hypersurfaces of high degree

2005-10-18

arxiv.org/abs/math/0510376v1

Mathematics

Algebraic Geometry

to appear in the "Annales de l'Institut Fourier"

Scientific paper

In this article, we prove that there does not exist a family of entire curves
in the universal family of hypersurfaces of degree $d\geq 2n$ in the complex
projective space ${\mathbb P}^n$. This can be seen as a weak version of the
Kobayashi conjecture asserting that a general projective hypersurface of high
degree is hyperbolic in the sense of Kobayashi.

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