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Displaying similar documents to “Determinants in the study of Thue's method and curves with prescribed singularities.”

Simple framed curve singularities

Victor Goryunov, Gabor Lippner (2008)

Banach Center Publications

Similarity:

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.

Families of smooth curves on surface singularities and wedges

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...

Curves in P(C) with 1-dimensional symmetry.

A. A. du Plessis, Charles Terence Clegg Wall (1999)

Revista Matemática Complutense

Similarity:

In a previous paper we showed that the existence of a 1-parameter symmetry group of a hypersurface X in projective space was equivalent to failure of versality of a certain unfolding. Here we study in detail (reduced) plane curves of degree d ≥ 3, excluding the trivial case of cones. We enumerate all possible group actions -these have to be either semisimple or unipotent- for any degree d. A 2-parameter group can only occur if d = 3. Explicit lists of singularities of the corresponding...

Real algebraic threefolds I. Terminal singularities.

János Kollár (1998)

Collectanea Mathematica

Similarity:

The aim of this series of papers is to develop the theory of minimal models for real algebraic threefolds. The ultimate aim is to understand the topology of the set of real points of real algebraic threefolds. We pay special attention to 3–folds which are birational to projective space and, more generally, to 3–folds of Kodaira dimension minus infinity.present work contains the beginning steps of this program. First we classify 3–dimensional terminal singularities over any field of characteristic...

Loop groups, elliptic singularities and principal bundles over elliptic curves

Stefan Helmke, Peter Slodowy (2003)

Banach Center Publications

Similarity:

There is a well known relation between simple algebraic groups and simple singularities, cf. [5], [28]. The simple singularities appear as the generic singularity in codimension two of the unipotent variety of simple algebraic groups. Furthermore, the semi-universal deformation and the simultaneous resolution of the singularity can be constructed in terms of the algebraic group. The aim of these notes is to extend this kind of relation to loop groups and simple elliptic singularities....