A note on the discriminant of a space curve
type: Item
instance of: scholarly article
title: A note on the discriminant of a space curve
zbMATH Open document ID: 0858.32031
DOI: 10.1007/BF02570469
author: Duco Van Straten
published in: Manuscripta Mathematica
publication date: 1995-08-29T00:00:00Z
full work available at URL: https://eudml.org/doc/156082
review text: Let \(X\to B\) be a deformation of a germ of an analytic space \(X_0\) over a smooth base germ. In many situations the discriminant \(\Delta\) is a hypersurface with remarkable properties, like being a free divisor (meaning that the module of vector fields on \(B\), logarithmic along \(\Delta\), is free). The author formulates a criterion for freeness of the discriminant in terms of relative \(T^1\)s. The author applies his criterion to space curves. The proof comes about from the combination of two facts. For families \(X\to S\) of curves with smooth general fibre the essential ingredient is that \(\omega^*_{X/S}\), the dual of the relative dualising sheaf, is flat over \(S\). On the other hand, this `\(\omega^*\)-constant' property holds quite general for codimension two Cohen-Macaulay germs.
reviewed by: Jan Stevens
Mathematics Subject Classification ID: 32S30
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14B12
zbMATH DE Number: 784069
zbMATH Keywords: free divisor
zbMATH Keywords: discriminant
zbMATH Keywords: space curves
MaRDI profile type: Publication
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OpenAlex ID: W2147414893
description: scientific article; zbMATH DE number 784069