8 papers
Invariants of real affine varieties based on their complexifications
Juliusz Banecki
We introduce a new family of invariants of real algebraic sets defined in terms of the topology of their complexifications and compute some of these invariants for spheres. This al…
Optimal embedding dimension in the Nash--Tognoli theorem
Juliusz Banecki
We prove that every smooth compact submanifold of can be approximated up to a small isotopy by the real locus of a nonsingular complex algebraic subset of $\C^n$ defined ove…
Homotopy properties of regular mappings into real retract rational varieties
Juliusz Banecki
We study homotopy properties of regular mappings from spheres into a real retract rational variety . We show that the homotopy classes which are represented by such mappings for…
Uniform rationality of products with the plane
Juliusz Banecki
Let be a nonsingular rational variety. We prove that is uniformly rational. It follows that nonsingular stably rational varieties are stably uniformly ra…
Retract rational varieties are uniformly retract rational
Juliusz Banecki
We prove that nonsingular retract rational algebraic varieties over any infinite field are uniformly retract rational. As a consequence, every rational, projective, nonsingular com…
Relative Stone-Weierstrass theorem for mappings between varieties
Juliusz Banecki
We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth m…