Milnor numbers for surface singularities (Q1972370)

In this interesting article the author studies the relationship between the topology of the Milnor fiber of a germ of a hypersurface function \(f\) and a partial resolution of the zero set of \(f\). More precisely he relates the Milnor number of \(f\) with the multiplicity of \(f\) generalized Milnor numbers of the projectivized tangent cone, and the strict transform of the first blowing-up-conjecture for any absolutely isolated singularity of a surface. He introduces the notion of a \(t\)-singularity. Much information for those \(t\)-singularities can be obtained from only the first two terms in a Taylor series of \(f\). In particular, a precise formula for the Milnor number of a \(t\)-singularity is given. In particular he gets a rather precise determinacy theorem. In the final section the author studies the global situation.