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arXiv · 1907.03249

Higher order polars of quasi-ordinary singularities

Evelia Rosa García Barroso·Janusz Gwoździewicz
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Abstract

A quasi-ordinary polynomial is a monic polynomial with coefficients in the power series ring such that its discriminant equals a monomial up to unit. In this paper we study higher derivatives of quasi-ordinary polynomials, also called higher order polars. We find factorizations of these polars. Our research in this paper goes in two directions. We generalize the results of Casas-Alvero and our previous results on higher order polars in the plane to irreducible quasi-ordinary polynomials. We also generalize the factorization of the first polar of a quasi-ordinary polynomial (not necessary irreducible) given by the first-named author and Gonz\'alez-P\'erez to higher order polars. This is a new result even in the plane case. Our results remain true when we replace quasi-ordinary polynomials by quasi-ordinary power series.

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Evelia Rosa García Barroso, Janusz Gwoździewicz. 2019-07-07. Higher order polars of quasi-ordinary singularities. https://doi.org/10.1093/imrn%2Frnaa106

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