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Displaying similar documents to “Some quantitative results in singularity theory”

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.

Singularities in drawings of singular surfaces

Alain Joets (2008)

Banach Center Publications

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When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and...

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....

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.