**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 H^{1}.
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).