Déformations de courbes avec action de groupe.
Nous étudions la théorie des déformations des revêtements galoisiens sauvagement ramifiés entre courbes stables. On examine d’abord les problèmes locaux, point double formel avec pour groupe d’inertie un -groupe, puis le cas global. On compare enfin les obstructions globales au relèvement aux obstructions locales.
We study deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates the deformation spaces. This cohomology turns out to be zero for all reductive linear free divisors and to be constructible for Koszul free divisors and weighted homogeneous free divisors.
We study compact Kähler manifolds admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of . We extend Calabi’s theorem on the structure of compact Kähler...