Hyperbolicity of general deformations

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We present two methods of constructing low degree Kobayashi hyperbolic hypersurfaces in the projective space: the projection method and the deformation method. The talk is based on joint works of the speaker with B. Shiffman and C. Ciliberto.
This is the content of the author's talk given at the conference "Effective Aspects of Complex Hyperbolic Varieties", Aber Wrac'h, France, September 10-14, 2007

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