Dominating real algebraic morphisms

2023/02/06 by Kucharz, Wojciech
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.02691

Abstract

Let X and Y be nonsingular real algebraic varieties, dimX>dimY-1. Assume that the variety Y is malleable, compact and connected. Our main result implies that each regular map from X to Y is homotopic to a surjective regular map. The class of malleable varieties includes all homogeneous spaces for linear real algebraic groups.

Related

• Piecewise-regular maps
• Spaces of maps between real algebraic varieties
• Relative Stone-Weierstrass theorem for mappings between varieties
• Holomorphic maps onto varieties of non-negative Kodaira dimension
• Andreotti-Frankel-Hamm theorem for morphisms of algebraic varieties