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Non-deformability of entire curves in projective hypersurfaces of high degree

Olivier Debarre; Gianluca Pacienza; Mihai Păun — 2006

Annales de l’institut Fourier

In this article, we prove that there does not exist a family of maximal rank of entire curves in the universal family of hypersurfaces of degree $d \geq 2 n$ in the complex projective space $ℙ^{n}$ . 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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