All these invariants can be computed from the Puiseux exponents and used to compute the Puiseux exponents. In addition, the delta--invariant, the resolution graph, and the spectrum of the singularity can be computed from the Puiseux exponents.
The algorithms for the computation of the spectrum is taken from [Saito, K: Exponents of an irreducible plane curve singularity. math.AG/0009133 ]. The remaining algorithms are contained in the book [deJong, Th. and G. Pfister: Local Analytic Geometry. Vieweg 2000].
In the second part conditions are given whether a surface in projective 3-space occurs as the determinant of a symmetric matrix with linear entries. In particular, such cubics and quartics are classified.
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