E. Ballico

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

abstract:
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).