Two classes of hyperbolic surfaces in P^3

Details Two classes of hyperbolic surfaces in P^3 Two classes of hyperbolic surfaces in P^3

1998-11-25

arxiv.org/abs/math/9811152v1

International J. Math. 11 (2000), 65-101.

Mathematics

Algebraic Geometry

Scientific paper

We construct two classes of singular Kobayashi hyperbolic surfaces in $P^3$. The first consists of generic projections of the cartesian square $V = C \times C$ of a generic genus $g \ge 2$ curve $C$ smoothly embedded in $P^5$. These surfaces have C-hyperbolic normalizations; we give some lower bounds for their degrees and provide an example of degree 32. The second class of examples of hyperbolic surfaces in $P^3$ is provided by generic projections of the symmetric square $V' = C_2$ of a generic genus $g \ge 3$ curve $C$. The minimal degree of these surfaces is 16, but this time the normalizations are not C-hyperbolic.

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