Haar spaces and polynomial selections.

Balaj, Mircea; Wa̧sowicz, Szymon

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Zbigniew Jelonek (1993)

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We describe the set of points over which a dominant polynomial map $f = (f_{1}, . . ., f_{n}) : ℂ^{n} \to ℂ^{n}$ is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by $(\prod_{i = 1}^{n} d e g f_{i} - μ (f)) / (m i n_{i = 1, . . ., n} d e g f_{i})$ .

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Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real...