C-pairs and their morphisms
Stefan Kebekus, Erwan Rousseau

TL;DR
This paper surveys Campana's theory of C-pairs in complex geometry, providing foundational definitions and a well-behaved notion of morphism to facilitate future research in hyperbolicity, rational points, and entire curves.
Contribution
It introduces a systematic framework for C-pairs and their morphisms, improving behavior in singular cases and connecting to minimal model theory.
Findings
Defines a new notion of morphism for C-pairs
Establishes functorial properties relating to minimal models
Serves as a comprehensive reference for future applications
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Nonlinear Waves and Solitons · Mathematics and Applications
