Currently displaying 1 – 18 of 18

Showing per page

Order by Relevance | Title | Year of publication

Rational functions without poles in a compact set

W. Kucharz — 2006

Colloquium Mathematicae

Let X be an irreducible nonsingular complex algebraic set and let K be a compact subset of X. We study algebraic properties of the ring of rational functions on X without poles in K. We give simple necessary conditions for this ring to be a regular ring or a unique factorization domain.

Nash cohomology of smooth manifolds

W. Kucharz — 2005

Annales Polonici Mathematici

A Nash cohomology class on a compact Nash manifold is a mod 2 cohomology class whose Poincaré dual homology class can be represented by a Nash subset. We find a canonical way to define Nash cohomology classes on an arbitrary compact smooth manifold M. Then the Nash cohomology ring of M is compared to the ring of algebraic cohomology classes on algebraic models of M. This is related to three conjectures concerning algebraic cohomology classes.

Approximation of holomorphic maps by algebraic morphisms

J. BochnakW. Kucharz — 2003

Annales Polonici Mathematici

Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.

Page 1

Download Results (CSV)