Displaying similar documents to “Haar spaces and polynomial selections.”

The set of points at which a polynomial map is not proper

Zbigniew Jelonek (1993)

Annales Polonici Mathematici


We describe the set of points over which a dominant polynomial map f = ( f 1 , . . . , f n ) : n 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 ( i = 1 n d e g f i - μ ( f ) ) / ( m i n i = 1 , . . . , n d e g f i ) .

Real and complex pseudozero sets for polynomials with applications

Stef Graillat, Philippe Langlois (2007)

RAIRO - Theoretical Informatics and Applications


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...