Low-dimensional singularities with free divisors as discriminants

authored by

Ragnarrolaf Buchweitz, Wolfgang Ebeling, Hans Christian Graf v. Bothmer

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.

Organisation(s)

Institute of Algebraic Geometry

External Organisation(s)

University of Toronto

Type

Article

Journal

Journal of Algebraic Geometry

Volume

18

Pages

371-406

No. of pages

36

ISSN

1056-3911

Publication date

2009

Publication status

Published

Peer reviewed

Yes

Electronic version(s)

https://doi.org/10.1090/S1056-3911-08-00508-0 (Access: Unknown)