Research Papers

Starting from 2009, I decided to keep track of the years in which the papers were originally written. Perhaps there are  some imprecisions before 2005. 

32. Foliations with trivial canonical bundle on Fano 3-folds. We classify the irreducible components of the space of foliations on Fano $3$-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of $3$-folds.
joint with F. Loray, F. Touzet
Submitted

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31. Singular foliations with trivial canonical class. This paper is devoted  to describe the structure of  singular codimension one foliations with  numerically trivial canonical bundle on projective manifolds. To achieve this goal  we  study the reduction modulo p of foliations, describe the structure of first integrals of (semi-)stable foliations with (negative) zero canonical bundle, establish a criterium for uniruledness of projective manifolds, and  investigate the deformation of free morphisms along foliations. This paper  also contains   new information about the structure of codimension one foliations on projective spaces of dimension n of degree smaller than or equal to 2n-3.
joint with F. Loray, F. Touzet
Submitted

30. Rigid flat webs on the projective plane.  This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit  a countable infinity  family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.
joint with D. Marin
Submitted

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29. Resonance webs of hyperplane arrangements. Each irreducible component of the first resonance variety of a hyperplane arrangement  naturally determines a codimension one foliation on the ambient space. The superposition of  these foliations define what we call the resonance  web of the arrangement. In this paper we initiate the study of these objects  with emphasis on their spaces of abelian relations.

2009

28. The characteristic variety of a generic foliation. We confirm a conjecture of  Bernstein and Lunts which predicts that the characteristic variety  of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and fibers over singular points.

27. Germs of integrable forms and varieties of minimal degree. We study the subvariety of  integrable 1-forms in a finite dimensional vector space W of germs of 1-forms. We prove that the irreducible components with dimension comparable with the rank of W are of minimal degree. 

26. Foliations invariant by rational maps.  We give a classification of pairs (foliation, rational map)  where the foliation is a  singular holomorphic foliation on a projective surface and the rational map is a non-invertible dominant rational map preserving the foliation. 

2008

2007

2005

2004

2003

2002

2001

2000