Abstract We consider differential forms associated to Campana’s geometric orbifolds from a new perspective, namely, as qfh-sheaf on the variety underlying orbifold. This approach avoids having choose covering of variety, which is one drawbacks common way work with these forms.

0 Introduction In this paper, we give an algorithm to compute the following cohomology groups on U = C n n V (f) for any non-zero polynomial f 2 Qx 1 ; : : : ; x n ]: 1. H k (U; C U), where C U is the constant sheaf on U with stalk C. 2. H k (U; V), where V is the locally constant sheaf on U of rank one deened by a multi-valued function f a 1 1 f a d d with polynomials f 1 ; : : : ; f d 2 Qx] s...

One of the main highlights of the previous semester was an interplay between the following objects: the nilpotent cone in g, the cotangent bundle T ∗(G/B), the universal enveloping algebra U(g) (or more precisely, its central reduction Uλ(g)) and the sheaf D G/B of λ-twisted differential operators on G/B. In our present story, Symn(C) is an analog of the nilpotent cone, Hilbn(C) is an analog of...