The Milnor Number and Deformations of Complex Curve Singularities.
Gert-Martin Greuel, Ragnar Buchweitz (1980)
Inventiones mathematicae
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Gert-Martin Greuel, Ragnar Buchweitz (1980)
Inventiones mathematicae
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Liang Chen (2016)
Open Mathematics
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In this paper, geometric properties of spacelike curves on a timelike surface in Lorentz-Minkowski 3-space are investigated by applying the singularity theory of smooth functions from the contact viewpoint.
E. Casas-Alvero (1990)
Mathematische Annalen
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Antonio Campillo (1988)
Banach Center Publications
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Gérard Gonzalez-Sprinberg, Monique Lejeune-Jalabert (1997)
Annales Polonici Mathematici
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Following the study of the arc structure of singularities, initiated by J. Nash, we give criteria for the existence of smooth curves on a surface singularity (S,O) and of smooth branches of its generic hypersurface section. The main applications are the following: the existence of a natural partition of the set of smooth curves on (S,O) into families, a description of each of them by means of chains of infinitely near points and their associated maximal cycle and the existence of smooth...
Maria Grazia Cinquegrani (1988)
Manuscripta mathematica
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Ulrich Karras (1980)
Mathematische Annalen
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Maciej Borodzik (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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We present an effective and elementary method of determining the topological type of a cuspidal plane curve singularity with given local parametrization.
Eduardo Casas (1983)
Manuscripta mathematica
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Buchner, Klaus (1997)
General Mathematics
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Bronislaw Wajnryb (1979)
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Jürgen Herzog, Rolf Waldi (1986)
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J.H.M. Steenbrink, A. Némethi (1996)
Mathematische Zeitschrift
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Jan Stevens (1984)
Mathematische Annalen
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Szymon Brzostowski, Tadeusz Krasiński (2014)
Open Mathematics
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The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.