General curves on algebraic surfaces

Abstract

We give upper bounds on the genus of a curve with general moduli assuming that it can be embedded in a projective nonsingular surface $Y$ so that $\dim (|C|)>0$. We find such bounds for all types of surfaces of intermediate Kodaira dimension and, under mild restrictions, for surfaces of general type whose minimal model $Z$ satisfies the Castelnuovo inequality $K_Z^2\ge 3\chi ({Ø}_Z)-10$. In this last case we obtain $g\le 19$. In the other cases considered the bounds are lower.

arXiv commentThe deformation theory part has been revised. All the rest is unchanged

Cited by in corpus (2)

• Some results on the second Gaussian map for curves
• On deformations of curves supported on rigid divisors