Abstract
We construct two classes of singular Kobayashi hyperbolic surfaces in ℙ3. The first consists of generic projections of the Cartesian square V = C × C of a generic genus g ≥ 2 curve C smoothly embedded in ℙ5. 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 ℙ3 is provided by generic projections of the symmetric square V′ = C2 of a generic genus g ≥ 3 curve C. The minimal degree of these surfaces is 16, but this time the normalizations are not C-hyperbolic.
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