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arXiv · 2410.00405

The Albanese of a C-pair

Stefan Kebekus·Erwan Rousseau
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Abstract

Written with a view toward applications in hyperbolicity, rational points, and entire curves, this paper addresses the problem of constructing Albanese maps within Campana's theory of C-pairs (or "geometric orbifolds"). It introduces C-semitoric pairs as analogs of the (semi)tori used in the classic Albanese theory and follows Serre by defining the Albanese of a C-pair as the universal map to a C-semitoric pairs. The paper shows that the Albanese exists in relevant cases, gives sharp existence criteria, and conjectures that a "weak Albanese" exists unconditionally.

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Stefan Kebekus, Erwan Rousseau. 2024-10-01. The Albanese of a C-pair. https://arxiv.org/abs/2410.00405

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