Topological moduli space for germs of holomorphic foliations III :: Complete families

David Marin Perez; Jean François Mattei; Éliane Salem

Topological moduli space for germs of holomorphic foliations III : Complete families

David Marin Perez, Jean François Mattei, Éliane Salem

Departamento de Matemáticas

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Resumen

In this work we use our previous results on the topological classifica- tion of generic singular foliation germs on (C2,0) to construct complete families: after fixing the semi-local topological invariants we prove the existence of a min- imal family of foliation germs that contains all the topological classes and such that any equisingular global family with parameter space an arbitrary complex manifold factorizes through it.

Idioma original	Inglés
Número de páginas	27
Publicación	Transactions of the American Mathematical Society
Estado	Aceptada en prensa - 2024

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https://ddd.uab.cat/record/293669Licencia: CC BY-NC-ND

ESTRUCTURAS Y DESIGUALDADES GEOMETRICAS UNIVERSALES
Solanes Farres, G. (Principal Investigator), Balacheff , F. N. (Investigador/a Principal 2), Gallego Gomez, E. (Investigador/a), Marin Perez, D. (Investigador/a), Nicolau Reig, M. (Investigador/a), Porti Pique, J. (Investigador/a), Trillo Gomez, J. A. (Colaborador/a), GIL MORENO DE MORA I SARDÀ, T. (Colaborador/a), Heusener, M. (Colaborador/a), Babenko, I. (Colaborador/a), Sabourau, S. (Colaborador/a), Tzanev, K. (Colaborador/a), Meersseman, L. (Colaborador/a), Bedrouni, S. (Colaborador/a), Faifman, D. (Colaborador/a), Wannerer, T. (Colaborador/a), Bernig, A. (Colaborador/a) & Fisac Cámara, D. (Colaborador/a)
1/09/22 → 31/08/25
Proyecto: Proyectos y Ayudas de Investigación

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title = "Topological moduli space for germs of holomorphic foliations III :: Complete families",

abstract = "In this work we use our previous results on the topological classifica- tion of generic singular foliation germs on (C2,0) to construct complete families: after fixing the semi-local topological invariants we prove the existence of a min- imal family of foliation germs that contains all the topological classes and such that any equisingular global family with parameter space an arbitrary complex manifold factorizes through it.",

keywords = "Complex dynamical systems, Complex ordinary differential equations, Holomorphic vector fields, Holomorphic foliations, Singularities, Holonomy, Moduli space, Complete families, Universal deformation",

author = "{Marin Perez}, David and Mattei, {Jean Fran{\c c}ois} and {\'E}liane Salem",

year = "2024",

language = "English",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

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TY - JOUR

T1 - Topological moduli space for germs of holomorphic foliations III :

T2 - Complete families

AU - Marin Perez, David

AU - Mattei, Jean François

AU - Salem, Éliane

PY - 2024

Y1 - 2024

N2 - In this work we use our previous results on the topological classifica- tion of generic singular foliation germs on (C2,0) to construct complete families: after fixing the semi-local topological invariants we prove the existence of a min- imal family of foliation germs that contains all the topological classes and such that any equisingular global family with parameter space an arbitrary complex manifold factorizes through it.

AB - In this work we use our previous results on the topological classifica- tion of generic singular foliation germs on (C2,0) to construct complete families: after fixing the semi-local topological invariants we prove the existence of a min- imal family of foliation germs that contains all the topological classes and such that any equisingular global family with parameter space an arbitrary complex manifold factorizes through it.

KW - Complex dynamical systems

KW - Complex ordinary differential equations

KW - Holomorphic vector fields

KW - Holomorphic foliations

KW - Singularities

KW - Holonomy

KW - Moduli space

KW - Complete families

KW - Universal deformation

M3 - Article

SN - 0002-9947

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -

Topological moduli space for germs of holomorphic foliations III : Complete families

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