Dominating real algebraic morphisms

TL;DR

This paper proves that under certain conditions, any regular map from a higher-dimensional real algebraic variety to a malleable, compact, connected variety can be homotoped to a surjective regular map, expanding understanding of algebraic morphisms.

Contribution

It establishes that all regular maps from certain high-dimensional varieties to malleable varieties are homotopic to surjective maps, generalizing previous results.

Findings

Any regular map from X to Y is homotopic to a surjective regular map.

Includes all homogeneous spaces for linear real algebraic groups as malleable varieties.

Provides a new approach to the surjectivity of algebraic morphisms in real algebraic geometry.

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.