Approximation of maps between real algebraic varieties

2024/07/22 by Banecki, Juliusz, Kucharz, Wojciech
#14P05 #14P99 #26C15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.15456

Abstract

A nonsingular real algebraic variety Y is said to have the approximation property if for every real algebraic variety X the following holds: if f:X-->Y is a Cⁱnf map that is homotopic to a regular map, then f can be approximated in the Cⁱnf topology by regular maps. In this paper, we characterize the varieties Y with the approximation property. We also characterize the varieties Y with the approximation property combined with a suitable interpolation condition. Some of our results have variants concerning the regular approximation of continuous maps defined on (possibly singular) real algebraic varieties.

Related

• On approximation of maps into real algebraic homogeneous spaces
• Approximation and homotopy in regulous geometry
• Approximation and homotopy in regulous geometry
• Approximation of maps from algebraic polyhedra to real algebraic varieties
• Approximation by piecewise-regular maps