IRREDUCIBILITY OF EQUISINGULAR FAMILIES OF CURVES-IMPROVED CONDITIONS.

In Keilen (2003) we gave sufficient conditions for the irreducibility of the family Virr([This symbol cannot be presented in ASCII format]l,...,[This symbol cannot be presented in ASCII format]r) of irreducible curves in the linear system \D\t with precisely r singular points of topological, respectively, analytical, types [This symbol cannot be presented in ASCII format]l,... ,[This symbol cannot be presented in ASCII format]r on several classes of smooth projective surfaces Σ. The conditions were of the form [This symbol cannot be presented in ASCII format] where τ* is some invariant of singularity types, KΣ is the canonical divisor of Σ, and γ is some constant. In the present paper we improve this condition, that is, the constant γ, by a factor of 9. [ABSTRACT FROM AUTHOR]