(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2005)
We consider a complex submanifold X of finite codimension in an infinite-dimensional complex projective space P and a holomorphic vector bundle E over X. Given a covering U of X with Zariski open sets, we define a subcomplex C(X, E) of the Čech complex corresponding to the vector bundle E and the covering U. For a special class of coverings U, we prove that the complex C(X, E) is acyclic when X is a complete intersection and P admits smooth partitions of unity.