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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

Moduli of nodal curves on smooth surfaces of general type