Moduli of nodal curves on smooth surfaces of general type.

In this paper we focus on the problem of computing the number of moduli of the so called Severi varieties (denoted by V_d(|D|)), which parametrize universal families of irreducible, d -nodal curves in a complete linear system |D|, on a smooth projective surface S of general type. We determine geometrical and numerical conditions on D and numerical conditions on d ensuring that such a number coincides with the dimension of such a variety. As related facts, we also determine some sharp results concerning the geometry of some Severi varieties.