Two classes of hyperbolic surfaces in P3
Bernard Shiffman and Mikhail Zaidenberg
Abstract
We construct two classes of singular Kobayashi
hyperbolic surfaces in P3. The first consists of generic
projections of the cartesian square of a generic genus g>1 curve
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 of a generic curve of genus g>2. The minimal degree of these
surfaces is 16, but this time the normalizations are not C-hyperbolic.
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