Deformations in the large of some complex manifolds, I

الأصل · EN

Main topic of the paper is the determination, for a compact complex manifold M, of the class of manifolds X which are deformation equivalent to it. If M is a complex torus, then also X is so. After describing the structure of principal holomorphic torus bundles over curves, a similar result (stability by deformations in the large) is obtained also for the latter class of manifolds. A section of the paper is devoted to the structure of principal holomorphic torus bundles over tori, establishing the Riemann bilinear relations, and exhibiting a so called Appell Humbert family, which could conjecturally give all small deformations. Finally, a general definition is given of so called Blanchard -Calabi manifolds, which, using an old construction of Sommese, show that the family of complex structures on the differentiable manifold underlying the product of a curve of genus g≥ 2 with a 2-dimensional complex torus admits several distinct deformation types.