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Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of $0$ in ${ℂ}^p$, for some $p\>0$) or differentiable (parametrized by an open neighborhood of $0$ in ${ℝ}^p$, for some $p\>0$) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point $t$ of the parameter space, the fiber over $t$ of the first family is biholomorphic to the fiber over $t$ of the second family. Then, under which conditions are the...

On utilise les variétés LV-M pour construire des compactifications équivariantes $M$ d’un groupe ${\left({ℂ}^{*}\right)}^m$ avec une variété d’Albanèse nulle mais telles que l’espace des formes holomorphes fermées de degré 1 soit non nul et de dimension inférieure à ${\dim }_{ℂ}{H}^1(M,{𝒪}_M)$.