Low-dimensional Singularities with Free Divisors as Discriminants
Abstract
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.
Cite
@article{arxiv.math/0612119,
title = {Low-dimensional Singularities with Free Divisors as Discriminants},
author = {Ragnar-Olaf Buchweitz and Wolfgang Ebeling and Hans-Christian Graf v. Bothmer},
journal= {arXiv preprint arXiv:math/0612119},
year = {2009}
}
Comments
29 pages, misprints and references corrected