We present versal complex analytic families, over a smooth base and of fibre
dimension zero, one, or two, where the discriminant constitutes a free divisor.
These families include finite flat maps, versal deformations of reduced curve
singularities, and versal deformations of Gorenstein surface singularities in
C^5. It is shown that such free divisors often admit a "fast normalization",
obtained by a single application of the Grauert-Remmert normalization
algorithm. For a particular Gorenstein surface singularity in C^5, namely the
simple elliptic singularity of type \tilde A_4, we exhibit an explicit
discriminant matrix and show that the slice of the discriminant for a fixed
j-invariant is the cone over the dual variety of an elliptic curve.Comment: 29 pages, misprints and references correcte
