Supplement to the paper “Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices” (Ann. Polon. Math. 101 (2011), 275–291)
Volume 103 / 2012
Annales Polonici Mathematici 103 (2012), 101-107
MSC: 14P15, 32B20, 26E10.
DOI: 10.4064/ap103-1-8
Abstract
In IMUJ Preprint 2009/05 we investigated the quasianalytic perturbation of hyperbolic polynomials and symmetric matrices by applying our quasianalytic version of the Abhyankar–Jung theorem from IMUJ Preprint 2009/02, whose proof relied on a theorem by Luengo on $\nu$-quasiordinary polynomials. But those papers of ours were suspended after we had become aware that Luengo's paper contained an essential gap. This gave rise to our subsequent article on quasianalytic perturbation theory, which developed, however, different methods and techniques. A recent paper by Parusiński–Rond validates Luengo's result, which allows us to resume our previous approach.
