Foliated affine and projective structures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916310913384448 |
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| author | Deroin, Bertrand Guillot, Adolfo |
| author_facet | Deroin, Bertrand Guillot, Adolfo |
| contents | We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them at singular points of the foliation, and we prove some index formulae in the case where the ambient manifold is compact. As a consequence of these, we establish that a regular foliation of general type on a compact algebraic manifold of even dimension does not admit a foliated projective structure. Finally, we classify foliated affine and projective structures along regular foliations on compact complex surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_04878 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Foliated affine and projective structures Deroin, Bertrand Guillot, Adolfo Differential Geometry Complex Variables 37F75, 53C12, 57M50 We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them at singular points of the foliation, and we prove some index formulae in the case where the ambient manifold is compact. As a consequence of these, we establish that a regular foliation of general type on a compact algebraic manifold of even dimension does not admit a foliated projective structure. Finally, we classify foliated affine and projective structures along regular foliations on compact complex surfaces. |
| title | Foliated affine and projective structures |
| topic | Differential Geometry Complex Variables 37F75, 53C12, 57M50 |
| url | https://arxiv.org/abs/2104.04878 |