Constructing low degree hyperbolic surfaces in P^3

Bernard Shiffman (1) , Mikhail Zaidenberg (2)

1 department of Mathematics
2 IF - Institut Fourier

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.

28, No.2, 377-388 (2002).

Mots clés: Projective surface; Kobayashi hyperbolic

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Bernard Shiffman, Mikhail Zaidenberg. Constructing low degree hyperbolic surfaces in P^3. Houston Journal of Mathematics, 2002, 28 (2), pp.377-388. ⟨hal-00323540⟩