Some obstructed equisingular families of curves on surfaces in projective three-space

Very few examples of obstructed equsingular families of curves on surfaces other than the projective plane are known. Combining results from Westenberger and Hirano with an idea from math.AG/9802009 we give in the present paper series of examples of families of irreducible curves with simple singularities on surfaces in projective three-space which are not T–smooth, i.e. do not have the expected dimension, and we compare this with conditions (showing the same asymptotics) which ensure the existence of a T–smooth component.