Scrolls and Hyperbolicity
نویسندگان
چکیده
Using degeneration to scrolls, we give an easy proof of non–existence of curves of low genera on general surfaces in P of degree d ≥ 5. We show, along the same lines, boundedness of families of curves of small enough genera on general surfaces in P. We also show that there exist Kobayashi hyperbolic surfaces in P of degree d = 7 (a result so far unknown), and give a new construction of such surfaces of degree d = 6. Finally we provide some new lower bounds for geometric genera of surfaces lying on general hypersurfaces of degree 3d ≥ 15 in P.
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