Work

Approximation of maps between real algebraic varieties

Year: 2025

Type: article

Abstract: A nonsingular real algebraic variety 𝑌 is said to have the approximation property if, for every nonsingular real algebraic variety 𝑋, the following holds: if f : X → Y f\colon X\rightarrow Y is a C ∞ \mathcal{C}^{\infty} map that is homotopic to a regular map, then 𝑓 can be approximated in the C ∞ \mathcal{C}^{\infty} 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.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2025-0005

Authors: Juliusz Banecki, Wojciech Kucharz

Institution: Jagiellonian University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funder: Narodowe Centrum Nauki