23\(^{\text{o}}\) colóquio Brasileiro de matemática (Q2753390)
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scientific article; zbMATH DE number 1668298
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 23\(^{\text{o}}\) colóquio Brasileiro de matemática |
scientific article; zbMATH DE number 1668298 |
Statements
4 November 2001
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curve singularity
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standard basis
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Milnor number
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algebroid curves
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ideal-theoretic algorithms
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formal power series rings
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Gröbner basis
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Tjurina numbers
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Kähler differentials
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1.0000001
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1.0000001
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1.0000001
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0.8149279
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23\(^{\text{o}}\) colóquio Brasileiro de matemática (English)
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The aim of this monograph is to describe how to compute several invariants of singularities of algebraic (or algebroid) curves using ideal-theoretic algorithms in formal power series rings. The algorithms involved are translations to the formal power series context of Gröbner basis theory, Robbiano-Sweedler's SAGBI (Subalgebra Analog to Gröbner Bases for Ideals) theory [\textit{L. Robbiano} and \textit{M. Sweedler}, Lect. Notes Math. 1430, 61-87 (1990)] and \textit{J. Miller}'s generalizations [\textit{J. Lyn Miller}, J. Symb. Comput. 21, No. 2, 139-153 (1996; Zbl 0867.13007)] . These algorithms are used to compute Milnor and Tjurina numbers, and objects related to the module of Kähler differentials of an algebroid curve.NEWLINENEWLINENEWLINEThe monograph is clearly written and is of interest not only for those working in the constructive theory of curve singularities but also for anyone who wants a concise account of knowledge of Gröbner basis and related methods in power series rings.
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