Definable Galois theory for bimeromorphic geometry
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912759026810880 |
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| author | Moosa, Rahim Pillay, Anand |
| author_facet | Moosa, Rahim Pillay, Anand |
| contents | The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal meromorphic bundles with algebraic structure group, and admitting no horizontal subvarieties, is deduced. Examples of algebraic groups arising as binding groups are provided, as is a characterisation of when they are linear. Using binding groups in CCM it is shown that, in contrast to the situation in differentially closed fields, there are many algebraic groups which admit nontrivial definable torsors over acl-closed sets in the theory DCCM of existentially closed differential CCM-structures. A self-contained exposition of the binding group theorem in totally transcendental theories, that emphasises the bitorsorial nature of the construction, is also included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Definable Galois theory for bimeromorphic geometry Moosa, Rahim Pillay, Anand Logic Complex Variables 03C45, 03C98, 32J99 The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal meromorphic bundles with algebraic structure group, and admitting no horizontal subvarieties, is deduced. Examples of algebraic groups arising as binding groups are provided, as is a characterisation of when they are linear. Using binding groups in CCM it is shown that, in contrast to the situation in differentially closed fields, there are many algebraic groups which admit nontrivial definable torsors over acl-closed sets in the theory DCCM of existentially closed differential CCM-structures. A self-contained exposition of the binding group theorem in totally transcendental theories, that emphasises the bitorsorial nature of the construction, is also included. |
| title | Definable Galois theory for bimeromorphic geometry |
| topic | Logic Complex Variables 03C45, 03C98, 32J99 |
| url | https://arxiv.org/abs/2508.19524 |