E. Ballico

The Non-Vanishing of First Cohomology Groups for Certain Infinite-Dimensional Complex Manifolds

Here, using the ideas of an old paper by S. Dineen (1976), we give large classes of pairs $(X,E)$ such that $X$ is an infinite-dimensional complex space very far from a Banach manifold, $E$ is a holomorphic vector bundle on $X$ and $H^1(X,E)$ is infinite-dimensional.

Infinite-dimensional complex manifold, first Cousin problem, additive Cousin problem, non-vanishing of cohomology.

MSC 2000: 32L05, 32K05