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Singular sets of holonomy maps for algebraic foliations

Gabriel CalsamigliaBertrand DeroinSidney FrankelAdolfo Guillot — 2013

Journal of the European Mathematical Society

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...

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