Degeneracy of entire curves in log surfaces with
We determine which algebraic surface of logarithmic irregularity admit an algebraically non-degenerate entire curve.
Degeneracy of holomorphic maps via orbifolds
We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.
Distribution des préimages et des points périodiques d’une correspondance polynomiale
Nous construisons pour toute correspondance polynomiale d’exposant de Lojasiewicz une mesure d’équilibre . Nous montrons que est approximable par les préimages d’un point générique et que les points périodiques répulsifs sont équidistribués sur le support de . En utilisant ces résultats, nous donnons une caractérisation des ensembles d’unicité pour les polynômes.
Distribution des valeurs des fonctions analytiques multiformes
Distribution laws for integrable eigenfunctions
We determine the asymptotics of the joint eigenfunctions of the torus action on a toric Kähler variety. Such varieties are models of completely integrable systems in complex geometry. We first determine the pointwise asymptotics of the eigenfunctions, which show that they behave like Gaussians centered at the corresponding classical torus. We then show that there is a universal Gaussian scaling limit of the distribution function near its center. We also determine the limit...