Related papers: Classification of absolutely dicritical foliations…
We show that the absolute period foliation of the principal stratum of abelian differentials on a surface of genus at least 3 is ergodic. We also investigate the absolute period foliation of affine invariant manifolds.
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R3 as the sum of the area integral and a non homogeneous term of suitable form. Here we consider the case of a class of…
A holomorphic foliation on $\mathbb P^2_{\mathbb C}$, or a real analytic foliation on $\mathbb{P}^{2}_{\mathbb{R}},$ is said to be convex if its leaves other than straight lines have no inflection points. The classification of the convex…
In this paper the detailed classification of three-dimensional exceptional canonical hypersurface singularities which don't satisfy the condition of well-formedness is given. This result completes the classification of three-dimensional…
This article studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we assume hypotheses on the reduction of singularities of the…
We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…
We show the existence of an essentially unique logarithmic model for any germ of non-dicritical singular holomorphic foliation of codimension one in $({\mathbb C}^n,0)$ without saddle-nodes.
We give a complete list of formal invariants for a large class of formal differential 1-forms $\w \in \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy$. \indent A $\hat{SL}$-equisingular deformation is an equireducible deformation which leaves…
For a complex surface of general type with a relatively minimal genus 2 fibration, the bounds of the orders of the automorphism group of the fibration, of its abelian subgroups and of its cyclic subgroups are determined as linear functions…
We study value semigroups associated to germs of maps $\mathbb{C} \rightarrow \mathbb{C}^3$ with fixed ramification profiles in a distinguished point. We then apply our analysis to deduce that Severi varieties of unicuspidal rational…
We prove that every topological conjugation between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugation which extends homeomorphically to the exceptional divisors of their minimal…
The surfaces of growing biological tissues, swelling gels, and compressed rubbers do not remain smooth, but frequently exhibit highly localized inward folds. We reveal the morphology of this surface folding in a novel experimental setup,…
We present examples of foliations with infinite dimensional basic symplectic and com- plex cohomologies, along with a general sufficient condition for such phenomena. This puts re- strictions on possible generalizations of several…
In this paper, we characterize the second bounded characteristic classes of foliated bundles in terms of the non-descendible quasi-morphisms on the universal covering of the structure group. As its application, we study the boundedness of…
We build a germ of singular foliation in dimension two with analytical class of separatrix and holonomy representations prescribed. Thanks to this construction, we study the link between moduli of a foliation and moduli of its separatrix.
We define tensor product decompositions of $E_0$-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that…
We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.
We prove for L-function attached to an automorphic cusp form for the Hecke congruence group $\Gamma_0(D)$, which is also an eigenfunction of all the Hecke operators, that a positive proportion of its non-trivial zeros lie on the critical…
Nous d\'ecrivons les singularit\'es de feuilletages holomorphes dicritiques de petite multiplicit\'e en dimension $3$. En particulier nous relions l'existence de d\'eformations et de d\'eploiements non triviaux \`a des probl\`emes…
A computable structure A is x-computably categorical for some Turing degree x, if for every computable structure B isomorphic to A there is an isomorphism f:B -> A with f computable in x. A degree x is a degree of categoricity if there is a…