Singular sets of holonomy maps for algebraic foliations

Calsamiglia, 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 -