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A note on square-free factorizations
(Łódź University Press, 2017)
We analyze properties of various square-free factorizations in greatest common divisor domains (GCD-domains) and domains satisfying the ascending chain condition for principal ideals (ACCP-domains).
Vector bundles and blowups
(Łódź University Press, 2017)
Let X be a nonsingular quasi-projective complex algebraic variety and let E be an algebraic vector bundle on X of rank r ≥ 2. The pullback of E by the blowup of X at a suitably chosen nonsingular subvariety of X of codimension ...
Bézout’s inequality for real polynomials
(Łódź University Press, 2017)
Let F(X, Y ), G(X, Y ) be polynomials of degrees m, n > 0 respectively. We prove, that the set {(x, y) Є R² : F(x, y) = G(x, y) = 0} has at most mn connected components.
Rationality of semialgebraic functions
(Łódź University Press, 2017)
Let X be an algebraic subset of Rⁿ, and ƒ: X → R a semialgebraic function. We prove that if ƒ is continuous rational on each curve C ⊂ X then: 1) ƒ is arc-analytic, 2) ƒ is continuous rational on X. As a consequence we ...
Divergence-free polynomial derivations
(Łódź University Press, 2017)
In this paper we present some new and old properties of divergences and divergence-free derivations.
Wielomiany i szeregi potęgowe
(Łódź University Press, 2017)
Formal and convergent solutions of analytic equations
(Łódź University Press, 2017)
We provide the detailed proof of a sharpened version of the
M. Artin Approximation Theorem.
On a generic symmetry defect hypersurface
(Łódź University Press, 2017)
We show that symmetry defect hypersurfaces for two generic members of the irreducible algebraic family of n-dimensional smooth irreducible subvarieties in general position in C²ⁿ are homeomorphic and they have homeomorphic ...
Polynomials and power series
(Łódź University Press, 2017)
Rational constants of cyclotomic derivations
(Łódź University Press, 2017)