The Albanese of a C-pair
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929585418928128 |
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| author | Kebekus, Stefan Rousseau, Erwan |
| author_facet | Kebekus, Stefan Rousseau, Erwan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_00405 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Albanese of a C-pair Kebekus, Stefan Rousseau, Erwan Algebraic Geometry Complex Variables 32C99, 32H99, 32A22 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. |
| title | The Albanese of a C-pair |
| topic | Algebraic Geometry Complex Variables 32C99, 32H99, 32A22 |
| url | https://arxiv.org/abs/2410.00405 |