C-pairs and their morphisms
Algebraic Geometry
2024-11-12 v2 Complex Variables
Abstract
This paper surveys Campana's theory of C-pairs (or "geometric orbifolds") in the complex-analytic setting, to serve as a reference for future work. Written with a view towards applications in hyperbolicity, rational points, and entire curves, it introduces the fundamental definitions of C-pair-theory systematically. In particular, it establishes an appropriate notion of "morphism", which agrees with notions from the literature in the smooth case, but is better behaved in the singular setting and has functorial properties that relate it to minimal model theory.
Cite
@article{arxiv.2407.10668,
title = {C-pairs and their morphisms},
author = {Stefan Kebekus and Erwan Rousseau},
journal= {arXiv preprint arXiv:2407.10668},
year = {2024}
}
Comments
Version 2: Add references and fix cross-references between the papers arXiv:2407.10668, arXiv:2410.01245, and arXiv:2410.00405