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Un exemple de feuilletage modulaire déduit d’une solution algébrique de l’équation de Painlevé VI

Gaël Cousin (2014)

Annales de l’institut Fourier

On peut construire facilement des exemples de connexions plates de rang 2 sur ℙ 2 comme tirés en arrière de connexions sur ℙ 1 . On donne un exemple de connexion qui ne peut être obtenue de cette manière. Cet exemple est construit à partir d’une solution algébrique de l’équation de Painlevé VI. On en déduit un feuilletage modulaire. La preuve de ce fait repose sur la classification des feuilletages sur les surfaces projectives par leurs dimensions de Kodaira, fruit du travail de Brunella, McQuillan et...

Universal isomonodromic deformations of meromorphic rank 2 connections on curves

Viktoria Heu (2010)

Annales de l’institut Fourier

We consider tracefree meromorphic rank 2 connections over compact Riemann surfaces of arbitrary genus. By deforming the curve, the position of the poles and the connection, we construct the global universal isomonodromic deformation of such a connection. Our construction, which is specific to the tracefree rank 2 case, does not need any Stokes analysis for irregular singularities. It is thereby more elementary than the construction in arbitrary rank due to B. Malgrange and I. Krichever and it includes...

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И.Н. Якушина (1990)

Zapiski naucnych seminarov Leningradskogo

[unknown]

Sébastien Alvarez, Nicolas Hussenot (0)

Annales de l’institut Fourier

Vector fields, invariant varieties and linear systems

Jorge Vitório Pereira (2001)

Annales de l’institut Fourier

We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criterion for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields, and a generalization of Darboux's criteria. We also provide a new proof of Gomez--Mont's result on foliations...

Vector fields, separatrices and Kato surfaces

Adolfo Guillot (2014)

Annales de l’institut Fourier

We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is compact). We also prove that, in a singular Stein surface endowed with a complete holomorphic vector field, a singular point of the surface where the zeros of the vector field do not accumulate is either a quasihomogeneous or a cyclic quotient singularity. We give...

Zeros of solutions of certain higher order linear differential equations

Hong-Yan Xu, Cai-Feng Yi (2010)

Annales Polonici Mathematici

We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + ⋯ + a ₁ ( z ) f ' + D ( z ) f = 0 , (1) where D ( z ) = Q ₁ ( z ) e P ₁ ( z ) + Q ₂ ( z ) e P ₂ ( z ) + Q ₃ ( z ) e P ₃ ( z ) , P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z), a j ( z ) (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.

Currently displaying 421 – 440 of 484