Vanishing Theorems on Compact Hermitian Symmetric Spaces.
Varietà complesse a struttura grassmanniana
We define and study the notions of connections and structures of grassmannian type on complex manifolds.
Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky
Nous construisons de nouvelles variétés complexes compactes comme espaces d’orbites d’actions linéaires de , généralisant en cela les constructions de Meersseman. Nous donnons également certaines propriétés de ces variétés.
Variétés sphériques de type A
Vector fields from locally invertible polynomial maps in ℂⁿ
Let (F₁,..., Fₙ): ℂⁿ → ℂⁿ be a locally invertible polynomial map. We consider the canonical pull-back vector fields under this map, denoted by ∂/∂F₁,...,∂/∂Fₙ. Our main result is the following: if n-1 of the vector fields have complete holomorphic flows along the typical fibers of the submersion , then the inverse map exists. Several equivalent versions of this main hypothesis are given.
Vector fields, invariant varieties and linear systems
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...
Version kählérienne d'une conjecture de Robert J. Zimmer