In this paper we focus on the problem of computing the number of moduli of the so called Severi varieties (denoted by V(|D|, \delta)), which parametrize universal families of irreducible, \delta-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 \delta ensuring that such number coincides with dim(V(|D|, \delta). As related facts, we also determines some sharp results concerning the geometry of some Severi varieties.
Categories: math.AG