A note on subvarieties of powers of OT-manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910566516260864 |
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| author | Moosa, Rahim Toma, Matei |
| author_facet | Moosa, Rahim Toma, Matei |
| contents | It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete. When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its cartesian powers have no interesting complex-analytic families of subvarieties. The methods of proof, which are similar to [Moosa, Moraru, and Toma ``An essentially saturated surface not of Kähler-type", {\em Bull. of the LMS}, 40(5):845--854, 2008], require studying finite unramified covers of OT-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on subvarieties of powers of OT-manifolds Moosa, Rahim Toma, Matei Complex Variables Algebraic Geometry Logic 32J18, 03C98 It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete. When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its cartesian powers have no interesting complex-analytic families of subvarieties. The methods of proof, which are similar to [Moosa, Moraru, and Toma ``An essentially saturated surface not of Kähler-type", {\em Bull. of the LMS}, 40(5):845--854, 2008], require studying finite unramified covers of OT-manifolds. |
| title | A note on subvarieties of powers of OT-manifolds |
| topic | Complex Variables Algebraic Geometry Logic 32J18, 03C98 |
| url | https://arxiv.org/abs/2408.08049 |