Local foliations with closed leaves

Abstract: Our goal is describing the leaf space of local holomorphic foliation whose leaves are closed in a neighborhood of the origin. By considering the holonomy groups associated to leaves, it is necessary to study the finitely generated groups of local biholomorphisms whose orbits are closed (or equivalently finite) in some neighborhood of the origin. We show that for such groups, there is always an analytic curve through the origin that is contained in the fixed point set of a finite index subgroup. Moreover, we outline the properties of the linear part of a local diffeomorphism with finite orbits. The result provides a stability result à la Reeb in intermediate dimension for dimension one foliations defined in the neighborhood of a compact invariant curve. This is a joint work with Lucivanio Lisboa and some of the results are part of his PhD thesis.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

Series comments: Subscribe the seminar mailing list, please send and email to brag-seminar-request@lists.ime.unicamp.br with "subscribe" in the subject line.

Previous talks available at the YouTube channel "Brazilian Algebraic Geometry" www.youtube.com/channel/UCM-pcdNdpWxQFgOg-illE2w