Classification of singularities at infinity of polynomials of degree 4 in two variables.

Siersma, Dirk; Smeltnik, Job

Displaying similar documents to “Classification of singularities at infinity of polynomials of degree 4 in two variables.”

Recognition of $𝒦$ -singularities of functions.

Tari, Farid (1992)

Experimental Mathematics

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Positivity of Thom polynomials II: the Lagrange singularities

Małgorzata Mikosz, Piotr Pragacz, Andrzej Weber (2009)

Fundamenta Mathematicae

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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.

On Thom Polynomials for A4(−) via Schur Functions

Öztürk, Özer (2007)

Serdica Mathematical Journal

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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....

Contact boundaries of hypersurface singularities and of complex polynomials

Clément Caubel, Mihai Tibăr (2003)

Banach Center Publications

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We survey some recent results concerning the behavior of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.

Differential spaces and singularities of space-time.

Buchner, Klaus (1997)

General Mathematics

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Some quantitative results in singularity theory

Y. Yomdin (2005)

Annales Polonici Mathematici

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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...

Constant Milnor Number Implies Constant Multiplicity for Quasihomogeneous Singularities.

Gert-Martin Greuel (1986)

Manuscripta mathematica

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Simple Singularities in Positive Characteristic.

G.M. Greuel, H. Kröning (1990)

Mathematische Zeitschrift

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Positivity of Schur function expansions of Thom polynomials

Piotr Pragacz, Andrzej Weber (2007)

Fundamenta Mathematicae

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Combining the approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of cone classes and positive polynomials for ample vector bundles, we show that the coefficients of the Schur function expansions of the Thom polynomials of stable singularities are nonnegative with positive sum.

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

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.

On the removal of subharmonic singularities of plurisubharmonic functions

E. M. Chirka (2003)

Annales Polonici Mathematici

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It is proved that any subharmonic function in a domain Ω ⊂ ℂⁿ which is plurisubharmonic outside of a real hypersurface of class C¹ is indeed plurisubharmonic in Ω.