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Constructing low degree hyperbolic surfaces in P^3

Bernard Shiffman·Mikhail Zaidenberg
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Abstract

We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a "hyperbolic non-percolation" property. We use this method to show that general small deformations of certain singular abelian surfaces of degree 8 are hyperbolic. We also show that a union of 15 planes in general position in projective 3-space admits hyperbolic deformations.

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Bernard Shiffman, Mikhail Zaidenberg. 2002-02-25. Constructing low degree hyperbolic surfaces in P^3. https://arxiv.org/abs/math/0202266

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