# Singular sets of holonomy maps for algebraic foliations

Gabriel Calsamiglia; Bertrand Deroin; Sidney Frankel; Adolfo Guillot

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 3, page 1067-1099
- ISSN: 1435-9855

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topCalsamiglia, Gabriel, et al. "Singular sets of holonomy maps for algebraic foliations." Journal of the European Mathematical Society 015.3 (2013): 1067-1099. <http://eudml.org/doc/277616>.

@article{Calsamiglia2013,

abstract = {In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty open set of singularities. The examples provided are based on the presence of sufficiently rich contracting dynamics in the holonomy pseudogroup of the foliation. This gives answers to some questions and conjectures of Loray and Ilyashenko, which follow-up on an approach to the associated ODE’s developed notably by Painlevé.},

author = {Calsamiglia, Gabriel, Deroin, Bertrand, Frankel, Sidney, Guillot, Adolfo},

journal = {Journal of the European Mathematical Society},

keywords = {holomorphic foliation; holonomy map; analytic extension; holomorphic foliation; holonomy map; analytic extension},

language = {eng},

number = {3},

pages = {1067-1099},

publisher = {European Mathematical Society Publishing House},

title = {Singular sets of holonomy maps for algebraic foliations},

url = {http://eudml.org/doc/277616},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Calsamiglia, Gabriel

AU - Deroin, Bertrand

AU - Frankel, Sidney

AU - Guillot, Adolfo

TI - Singular sets of holonomy maps for algebraic foliations

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 3

SP - 1067

EP - 1099

AB - In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty open set of singularities. The examples provided are based on the presence of sufficiently rich contracting dynamics in the holonomy pseudogroup of the foliation. This gives answers to some questions and conjectures of Loray and Ilyashenko, which follow-up on an approach to the associated ODE’s developed notably by Painlevé.

LA - eng

KW - holomorphic foliation; holonomy map; analytic extension; holomorphic foliation; holonomy map; analytic extension

UR - http://eudml.org/doc/277616

ER -

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