Constructing low degree hyperbolic surfaces in P^3

Details Constructing low degree hyperbolic surfaces in P^3 Constructing low degree hyperbolic surfaces in P^3

2002-02-25

arxiv.org/abs/math/0202266v1

Houston J. of Math. 28, Special issue for S. S. Chern, (2002), 377-388.

Mathematics

Algebraic Geometry

9 pages, to appear in Chern issue of Houston J. Math

Scientific paper

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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