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Consider the family S of irreducible plane curves of degree n with d nodesand k cusps as singularities. Let W be an irreducible component of S. Weconsider the natural rational map from W to the moduli space of curves of genusg=(n-1)(n-2)/2-d-k. We define the "number of moduli of W" as the dimension ofthe image of W with respect to this map. If W has the expected dimension equalto 3n+g-1-k, then the number of moduli of W is at most equal to the min(3g-3,3g-3+\rho-k), dove \rho is the Brill-Neother number of the linear series ofdegree n and dimension 2 on a smooth curve of genus g. We say that W has theexpected number of moduli if the equality holds. In this paper we constructexamples of families of irreducible plane curves with nodes and cusps assingularities having expected number of moduli and with non-positiveBrill-Noether number.

Number of moduli of irreducible families of plane curves with nodes and cusps