E. Ballico

Branched coverings and minimal free resolution for
infinite-dimensional complex spaces

We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V) (e.g. complete intersections or cones over finite-dimensional projective spaces). In the former case we obtain the vanishing result for H1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V).