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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

Foliated affine and projective structures

Structures affines et projectives feuilletées

Résumé

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.
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Dates et versions

hal-03852390 , version 1 (15-11-2022)

Identifiants

  • HAL Id : hal-03852390 , version 1

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Bertrand Deroin, Adolfo Guillot. Foliated affine and projective structures. 2022. ⟨hal-03852390⟩
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