Low-dimensional singularities with free divisors as discriminants

verfasst von

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.

Organisationseinheit(en)

Institut für Algebraische Geometrie

Externe Organisation(en)

University of Toronto

Typ

Artikel

Journal

Journal of Algebraic Geometry

Band

18

Seiten

371-406

Anzahl der Seiten

36

ISSN

1056-3911

Publikationsdatum

2009

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

Elektronische Version(en)

https://doi.org/10.1090/S1056-3911-08-00508-0 (Zugang: Unbekannt)