Tjurina number of a generic irreducible curve singularity
type: Item
instance of: scholarly article
title: Tjurina number of a generic irreducible curve singularity
zbMATH Open document ID: 0892.14015
author: Rosa Peraire
published in: Journal of Algebra
publication date: 1998-07-27T00:00:00Z
review text: Let \(\gamma\) be an irredcible germ of plane analytic curve with equation \(f=0\) and let \(\tau(\gamma)= \dim_\mathbb{C} \mathbb{C}\{x,y\}/(f, f_y',f_x')\) be the Tjurina number of \(\gamma\). Various algorithms are known to compute Tjurina numbers of germs of plane curves having particular semigroups. In the present paper the author presents an algorithm that, starting from the semigroup of \(\gamma\), computes \(\tau(\gamma)\) and allows her to determine a \(\mathbb{C}\)-basis of \(\mathbb{C}\{x,y\}/(f, f_y',f_x')\). Moreover, by the upper semicontinuity of \(\tau (\gamma)\), the author obtains the minimum Tjurina number in the equisingularity class of \(\gamma\); this gives the dimension of the generic component of the moduli space of irreducible curves with fixed semigroup. An implementation of the algorithm (written by the author and \textit{J. Elias}) in a Mathematica package is also available.
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 1089117
zbMATH Keywords: Mathematica
zbMATH Keywords: plane analytic curve
zbMATH Keywords: Tjurina number
zbMATH Keywords: equisingularity class
zbMATH Keywords: component of the moduli space
reviewed by: Caterina Cumino
describes a project that uses: Mathematica
MaRDI profile type: Publication
OpenAlex ID: W2050623489
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DOI: 10.1006/JABR.1997.7073
description: scientific article; zbMATH DE number 1089117