Pull-back of singular levi-flat hypersurfaces

Andrés Beltrán; Arturo Fernández-Pérez; Hernán Neciosup

doi:10.4310/ARKIV.2021.V59.N2.A3

Pull-back of singular levi-flat hypersurfaces

Andrés Beltrán
, Arturo Fernández-Pérez
, Hernán Neciosup

Research output: Contribution to journal › Article › peer-review

Abstract

We study singular real analyti Levi-flat subsets invariant by singular holo-morphi foliations in omplex projetive spaes. We give suffiient onditions for a real analyti Levi-flat subset to be the pull-bak of a semianalyti Levi-flat hypersurfae in a omplex projetive surfae under a rational map or to be the pull-bak of a real algebrai urve under a meromorphi funtion. In partiular, we give an appliation to the ase of a singular real analyti Levi-flat hypersurfae. Our results improve previous ones due to Lebl and Bretas–Fernández-Pérez–Mol.

Original language	English
Pages (from-to)	307-321
Number of pages	15
Journal	Arkiv for Matematik
Volume	59
Issue number	2
DOIs	https://doi.org/10.4310/ARKIV.2021.V59.N2.A3
State	Published - 2021
Externally published	Yes

Keywords

Holomorphi foliations
Levi-flat subsets

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10.4310/ARKIV.2021.V59.N2.A3

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title = "Pull-back of singular levi-flat hypersurfaces",

abstract = "We study singular real analyti Levi-flat subsets invariant by singular holo-morphi foliations in omplex projetive spaes. We give suffiient onditions for a real analyti Levi-flat subset to be the pull-bak of a semianalyti Levi-flat hypersurfae in a omplex projetive surfae under a rational map or to be the pull-bak of a real algebrai urve under a meromorphi funtion. In partiular, we give an appliation to the ase of a singular real analyti Levi-flat hypersurfae. Our results improve previous ones due to Lebl and Bretas–Fern{\'a}ndez-P{\'e}rez–Mol.",

keywords = "Holomorphi foliations, Levi-flat subsets",

author = "Andr{\'e}s Beltr{\'a}n and Arturo Fern{\'a}ndez-P{\'e}rez and Hern{\'a}n Neciosup",

year = "2021",

doi = "10.4310/ARKIV.2021.V59.N2.A3",

language = "English",

volume = "59",

pages = "307--321",

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TY - JOUR

T1 - Pull-back of singular levi-flat hypersurfaces

AU - Beltrán, Andrés

AU - Fernández-Pérez, Arturo

AU - Neciosup, Hernán

PY - 2021

Y1 - 2021

N2 - We study singular real analyti Levi-flat subsets invariant by singular holo-morphi foliations in omplex projetive spaes. We give suffiient onditions for a real analyti Levi-flat subset to be the pull-bak of a semianalyti Levi-flat hypersurfae in a omplex projetive surfae under a rational map or to be the pull-bak of a real algebrai urve under a meromorphi funtion. In partiular, we give an appliation to the ase of a singular real analyti Levi-flat hypersurfae. Our results improve previous ones due to Lebl and Bretas–Fernández-Pérez–Mol.

AB - We study singular real analyti Levi-flat subsets invariant by singular holo-morphi foliations in omplex projetive spaes. We give suffiient onditions for a real analyti Levi-flat subset to be the pull-bak of a semianalyti Levi-flat hypersurfae in a omplex projetive surfae under a rational map or to be the pull-bak of a real algebrai urve under a meromorphi funtion. In partiular, we give an appliation to the ase of a singular real analyti Levi-flat hypersurfae. Our results improve previous ones due to Lebl and Bretas–Fernández-Pérez–Mol.

KW - Holomorphi foliations

KW - Levi-flat subsets

UR - https://www.scopus.com/pages/publications/85121030657

U2 - 10.4310/ARKIV.2021.V59.N2.A3

DO - 10.4310/ARKIV.2021.V59.N2.A3

M3 - Article

AN - SCOPUS:85121030657

SN - 0004-2080

VL - 59

SP - 307

EP - 321

JO - Arkiv for Matematik

JF - Arkiv for Matematik

IS - 2

ER -

Pull-back of singular levi-flat hypersurfaces

Abstract

Keywords

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