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LVMB manifolds and simplicial spheres

Jérôme Tambour (2012)

Annales de l’institut Fourier

LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of this generalization....

Minimal, rigid foliations by curves on n

Frank Loray, Julio C. Rebelo (2003)

Journal of the European Mathematical Society

We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space n for every dimension n 2 and every degree d 2 . Precisely, we construct a foliation which is induced by a homogeneous vector field of degree d , has a finite singular set and all the regular leaves are dense in the whole of n . Moreover, satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if is conjugate to another holomorphic foliation...

Monodromy and topological classification of germs of holomorphic foliations

David Marín, Jean-François Mattei (2012)

Annales scientifiques de l'École Normale Supérieure

We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representations whose topological invariance was conjectured in the eighties by Cerveau and Sad and is proved here under mild hypotheses.

Naive boundary strata and nilpotent orbits

Matt Kerr, Gregory Pearlstein (2014)

Annales de l’institut Fourier

We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups S U ( 2 , 1 ) , S p 4 , and G 2 .

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