SCROLLS AND HYPERBOLICITY.

Using degeneration to scrolls, we give an easy proof of non-existence of curves of low genera on general surfaces in ℙ³ of degree d ≥ 5. We also show that there exist Kobayashi hyperbolic surfaces in ℙ³ 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 ℙ4. [ABSTRACT FROM AUTHOR]