The Albanese of a C-pair

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.

arXiv commentVersion 2: Fix cross-references between the papers arXiv:2407.10668, arXiv:2410.01245, and arXiv:2410.00405. Add an example highlighting differences between various notions of irregularity. Add a brief appendix on the simplicity of general Prym varieties