Drawing bers embeddings of the Teichmüller space of once-punctured tori.
Du Bois invariants of isolated complete intersection singularities
We define Du Bois invariants for isolated singularities of complex spaces. We relate them to the Hodge numbers of the local and vanishing cohomology groups. Our main results express the Tjurina number of certain Gorenstein singularities in terms of Du Bois invariants and Hodge numbers of the link, and express the Hodge numbers of the Milnor fibre of certain three-dimensional complete intersections in similar terms. We also address the question of the semicontinuity of the Du Bois invariants under...
Dual of the space of holomorphic functions with continuous boundary values on a strictly pseudo-convex domain in Cn.
Dualität in der Funktionentheorie.
Dualität in der lokalen Kohomologie isolierter Singularitäten.
Dualité et comparaison pour les complexes de de Rham logarithmiques par rapport aux diviseurs libres
Soit une variété analytique complexe lisse et un diviseur libre. Les connexions logarithmiques intégrables par rapport à peuvent être étudiées comme des -modules localement libres munis d’une structure de module (à gauche) sur l’anneau des opérateurs différentiels logarithmiques . Dans cet article nous étudions deux résultats liés : la relation entre les duaux d’une connexion logarithmique intégrable sur les anneaux de base et , et un critère différentiel pour le théorème de comparaison...
Dualite pour les feuilletages transversalement holomorphes.
Dualité relative en géométrie analytique complexe.
Duality and distribution cohomology of manifolds
Duality and Intersection Theory in Complex Manifolds. I.
Duality and the DeRham Cohomology of Infinitesimal Neighborhoods.
Duality on complex spaces
Duality theorems for Hardy and Bergman spaces on convex domains of finite type in
We study Hardy, Bergman, Bloch, and BMO spaces on convex domains of finite type in -dimensional complex space. Duals of these spaces are computed. The essential features of complex domains of finite type, that make these theorems possible, are isolated.
Dynamics in the moduli space of Abelian differentials.
Dynamics of meromorphic maps with small topological degree III: geometric currents and ergodic theory
We continue our study of the dynamics of mappings with small topological degree on projective complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic “equilibrium” measure for each such mapping. Here we study the dynamical properties of this measure in detail: we give optimal bounds for its Lyapunov exponents, prove that it has maximal entropy, and show that it has product structure in the natural extension. Under a natural further assumption, we show that saddle points...
Dynamics of one-resonant biholomorphisms
Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in whose differentials have one-dimensional family of resonances in the first eigenvalues, (but more resonances are allowed for other eigenvalues). Next, we provide invariants and give conditions for the existence of basins of attraction. Finally, we give applications and examples demonstrating the sharpness of our conditions.
Dynamics of symmetric holomorphic maps on projective spaces.
We consider complex dynamics of a critically finite holomorphic map from Pk to Pk, which has symmetries associated with the symmetric group Sk+2 acting on Pk, for each k ≥1. The Fatou set of each map of this family consists of attractive basins of superattracting points. Each map of this family satisfies Axiom A.
Dynamics on Thurston's sphere of projective measured foliations.
Dynamics semi-conjugated to a subshift for some polynomial mappings in C2.
We study the dynamics near infinity of polynomial mappings f in C2. We assume that f has indeterminacy points and is non constant on the line at infinity L∞. If L∞ is f-attracting, we decompose the Green current along itineraries defined by the indeterminacy points and their preimages. The symbolic dynamics that arises is a subshift on an infinite alphabet.