Classification of flat pencils of foliations on compact complex surfaces
Annales de l'Institut Fourier, Volume 70 (2020) no. 5, pp. 2191-2214.

Related to the classification of regular foliations in a complex algebraic surface, we address the problem of classifying the complex surfaces which admit a flat pencil of foliations. On this matter, a classification of flat pencils which admit foliations with a first integral of genus one and isolated singularities was done by Lins Neto. In this work, we complement Lins Neto’s work, by obtaining the classification of compact complex surfaces which have a pencil with an invariant tangency set.

En lien avec la classification des feuilletages réguliers dans une surface algébrique complexe, on traite le problème de la classification des surfaces complexes qui admettent un pinceau plat de feuilletages. À propos de cette question, une classification des pinceaux plats qui admettent des feuilletages avec une intégrale première de genre un et des singularités isolées a été obtenue par Lins Neto. Dans ce travail, on complète le travail de Lins Neto, en obtenant la classification des surfaces complexes compactes qui ont un pinceau avec ensemble de tangence invariant.

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DOI: 10.5802/aif.3353
Classification: 34C07, 14J27, 14D06, 32S65
Keywords: compact complex surfaces, pencil of foliations, first integrals
Puchuri, Liliana 1

1 Pontificia Universidad Católica del Perú & Instituto de Matématica and Ciencias Afines (IMCA) Av Universitaria 1801, Lima (Peru)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Puchuri, Liliana. Classification of flat pencils of foliations on compact complex surfaces. Annales de l'Institut Fourier, Volume 70 (2020) no. 5, pp. 2191-2214. doi : 10.5802/aif.3353. https://aif.centre-mersenne.org/articles/10.5802/aif.3353/

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