Displaying similar documents to “Polar quotients and singularities at infinity of polynomials in two complex variables”

On Thom Polynomials for A4(−) via Schur Functions

Öztürk, Özer (2007)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45. We study the structure of the Thom polynomials for A4(−) singularities. We analyze the Schur function expansions of these polynomials. We show that partitions indexing the Schur function expansions of Thom polynomials for A4(−) singularities have at most four parts. We simplify the system of equations that determines these polynomials and give a recursive description of Thom polynomials for A4(−) singularities....

Positivity of Thom polynomials II: the Lagrange singularities

Małgorzata Mikosz, Piotr Pragacz, Andrzej Weber (2009)

Fundamenta Mathematicae

Similarity:

We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of the Thom polynomials of Lagrange singularities always have nonnegative coefficients. This is an analog of a result on the Thom polynomials of mapping singularities and Schur S-functions, established formerly by the last two authors.

Geometry of Puiseux expansions

Maciej Borodzik, Henryk Żołądek (2008)

Annales Polonici Mathematici

Similarity:

We consider the space Curv of complex affine lines t ↦ (x,y) = (ϕ(t),ψ(t)) with monic polynomials ϕ, ψ of fixed degrees and a map Expan from Curv to a complex affine space Puis with dim Curv = dim Puis, which is defined by initial Puiseux coefficients of the Puiseux expansion of the curve at infinity. We present some unexpected relations between geometrical properties of the curves (ϕ,ψ) and singularities of the map Expan. For example, the curve (ϕ,ψ) has a cuspidal singularity iff it...

Critical portraits for postcritically finite polynomials

Alfredo Poirier (2009)

Fundamenta Mathematicae

Similarity:

We extend the work of Bielefeld, Fisher and Hubbard on critical portraits to arbitrary postcritically finite polynomials. This gives the classification of such polynomials as dynamical systems in terms of their external ray behavior.

Some quantitative results in singularity theory

Y. Yomdin (2005)

Annales Polonici Mathematici

Similarity:

The classical singularity theory deals with singularities of various mathematical objects: curves and surfaces, mappings, solutions of differential equations, etc. In particular, singularity theory treats the tasks of recognition, description and classification of singularities in each of these cases. In many applications of singularity theory it is important to sharpen its basic results, making them "quantitative", i.e. providing explicit and effectively computable estimates for all...

The jump of the Milnor number in the X 9 singularity class

Szymon Brzostowski, Tadeusz Krasiński (2014)

Open Mathematics

Similarity:

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.

Deformation of polar methods

David B. Massey, Dirk Siersma (1992)

Annales de l'institut Fourier

Similarity:

We study deformations of hypersurfaces with one-dimensional singular loci by two different methods. The first method is by using the Le numbers of a hypersurfaces singularity — this falls under the general heading of a “polar” method. The second method is by studying the number of certain special types of singularities which occur in generic deformations of the original hypersurface. We compare and contrast these two methods, and provide a large number of examples.