Linear-type maps between affine and projective spaces
Algebraic Geometry
2023-07-28 v4
Abstract
We determine those maps between affine or projective spaces that are linear in the abstract sense of transforming collinear points into collinear points and whose restriction to any line is constant or injective. Our results are extensions of the classical Fundamental Theorems of Affine and Projective Geometries.
Cite
@article{arxiv.2204.10594,
title = {Linear-type maps between affine and projective spaces},
author = {Juan B. Sancho de Salas},
journal= {arXiv preprint arXiv:2204.10594},
year = {2023}
}
Comments
The old version has been split into two different articles. The first one, titled The Fundamental Theorem of Affine Geometry, appears in Extracta Mathematicae. The rest of the old version is now expanded with a new title