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Nondeformability of entire curves in projective hypersurfaces of high degree

Olivier Debarre·Gianluca Pacienza·Mihai Paun
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Abstract

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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Olivier Debarre, Gianluca Pacienza, Mihai Paun. 2005-10-18. Nondeformability of entire curves in projective hypersurfaces of high degree. https://arxiv.org/abs/math/0510376

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