Normal forms and moduli spaces of curve singularities with semigroup
Ignacio Luengo, Gerhard Pfister (1990)
Compositio Mathematica
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Ignacio Luengo, Gerhard Pfister (1990)
Compositio Mathematica
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Hans Olav Heröy (1989)
Mathematica Scandinavica
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Bernd Ulrich (1982)
Manuscripta mathematica
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Gerd Faltings (1997)
Journal für die reine und angewandte Mathematik
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Bernd Martin (1993)
Mathematische Zeitschrift
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Marius van der Put (2011)
Banach Center Publications
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This paper is a sequel to [vdP-Sa] and [vdP]. The two classes of differential modules (0,-,3/2) and (-,-,3), related to PII, are interpreted as fine moduli spaces. It is shown that these moduli spaces coincide with the Okamoto-Painlevé spaces for the given parameters. The geometry of the moduli spaces leads to a proof of the Painlevé property for PII in standard form and in the Flaschka-Newell form. The Bäcklund transformations, the rational solutions and the Riccati solutions for PII...
Stephen S.-T. Yau, John N. Mather (1982)
Inventiones mathematicae
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Bronislaw Wajnryb (1979)
Mathematische Annalen
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Peter M. Schuster (1997)
Manuscripta mathematica
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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.
António Araújo, Orlando Neto (2009)
Annales de la faculté des sciences de Toulouse Mathématiques
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We construct the generic component of the moduli space of the germs of Legendrian curves with generic plane projection topologically equivalent to a curve .
Victor Goryunov, Gabor Lippner (2008)
Banach Center Publications
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We obtain a complete list of simple framed curve singularities in ℂ² and ℂ³ up to the framed equivalence. We also find all the adjacencies between simple framed curves.
T. Figiel (1976)
Studia Mathematica
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Thomas Bayer (2003)
Revista Matemática Complutense
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We present algorithms and their implementation in the computer algebra system Singular 2.0 for the computation of equations for moduli spaces for semiquasihomogeneous singularities w.r.t. right equivalence. In addition, we describe the structure of the stabilizer group of Brieskorn-Pham singularities.