∗The author supported by Contract NSFR MM 402/1994.In this paper we find a global sufficient condition for suitable subschemes of Fano manifolds to be Nadel’s subschemes. We apply this condition to one-dimensional subschemes of a projective space.
We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence à la Galois.