English

Abstract Projective Lines

Algebraic Geometry 2009-12-07 v1

Abstract

We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that of a groupoid, with certain properties. This leads to a natural notion of bundle of projective lines, forming a stack.

Keywords

Cite

@article{arxiv.0912.0822,
  title  = {Abstract Projective Lines},
  author = {Anders Kock},
  journal= {arXiv preprint arXiv:0912.0822},
  year   = {2009}
}
R2 v1 2026-06-21T14:19:35.384Z