Using degeneration to scrolls, we give an easy proof of non-existence of curves of low genera on general surfaces in P-3 of degree d >= 5. We also show that there exist Kobayashi hyperbolic surfaces in P-3 of degree d = 7 (a result so far unknown), and give a new construction of such surfaces of degree d = 6. Our method yields also some lower bounds for geometric genera of surfaces lying on general hypersurfaces of degree 3d >= 15 in P-4.
Ciliberto, C., Zaidenberg, M. (2013). Scrolls and hyperbolicity. INTERNATIONAL JOURNAL OF MATHEMATICS, 24(4) [10.1142/S0129167X13500262].
Scrolls and hyperbolicity
CILIBERTO, CIRO;
2013-01-01
Abstract
Using degeneration to scrolls, we give an easy proof of non-existence of curves of low genera on general surfaces in P-3 of degree d >= 5. We also show that there exist Kobayashi hyperbolic surfaces in P-3 of degree d = 7 (a result so far unknown), and give a new construction of such surfaces of degree d = 6. Our method yields also some lower bounds for geometric genera of surfaces lying on general hypersurfaces of degree 3d >= 15 in P-4.File in questo prodotto:
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