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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 2 n in the complex projective space 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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