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On Thom Polynomials for A4(−) via Schur Functions

Öztürk, Özer (2007)

Serdica Mathematical Journal

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. We also give Thom polynomials...

On total reality of meromorphic functions

Alex Degtyarev, Torsten Ekedahl, Ilia Itenberg, Boris Shapiro, Michael Shapiro (2007)

Annales de l’institut Fourier

We show that, if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points, then it is conjugate to a real meromorphic function by a suitable projective automorphism of the image.

On triple curves through a rational triple point of a surface

M. R. Gonzalez-Dorrego (2006)

Annales Polonici Mathematici

Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.

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