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 $K_Z^2 \ge 3\chi(\O_Z) - 10$. In this last case we obtain $g \le 19$. In the other cases considered the bounds are lower.

SERNESI E (2015). General curves on algebraic surfaces. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 700, 209-233 [10.1515/crelle-2013-0019].

### 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 $K_Z^2 \ge 3\chi(\O_Z) - 10$. In this last case we obtain $g \le 19$. In the other cases considered the bounds are lower.
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SERNESI E (2015). General curves on algebraic surfaces. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 700, 209-233 [10.1515/crelle-2013-0019].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/142671
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