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C-pairs and their morphisms

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arxiv 2407.10668 v2 pith:4QT7DLJE submitted 2024-07-15 math.AG math.CV

Stefan Kebekus , Erwan Rousseau This is my paper · ORCID
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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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  1. Extension of adapted differentials on klt orbifolds

    math.AG 2024-11 conditional novelty 4.0 of 10

    Adapted reflexive 1-forms on klt Campana orbifolds extend to regular 1-forms on log resolutions of adapted covers, and induce pull-back morphisms for orbifold differentials.

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