Real Algebraic and Analytic Geometry
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323. Krzysztof Jan Nowak:
Supplement to the paper "Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices".

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Submission: 2011, May 11.

Abstract:
In paper~\cite{Now2}, we had investigated the quasianalytic perturbation of hyperbolic polynomials, applying our quasianalytic version of the Abhyankar--Jung theorem~\cite{Now1} whose proof relied on a theorem by Luengo~\cite{Lu} on $\nu$-quasiordinary polynomials. But our papers were suspended after we had become aware that paper~\cite{Lu} contained an essential gap. This gave rise to our subsequent article~\cite{Now3} which developed, however, different methods and techniques. The recent paper~\cite{Par-R} by Parusi\'{n}ski--Rond validates Luengo's result, which allows us to resume our previous approach.

Mathematics Subject Classification (2010): 14P15, 32B20, 15A18, 26E10.

Keywords and Phrases: quasianalytic functions, hyperbolic quasiordinary polynomials.

Full text, 9p.: dvi 30k, pdf 244k.