  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 show, along
the same lines, boundedness of families of curves of small enough genera on
general surfaces in P3. 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. Finally we provide some new
lower bounds for geometric genera of surfaces lying on general hypersurfaces of
degree 3d > 15 in P4.
