Perverse sheaves and higher-dimensional generzlization of Deligne's construction

Let us be given a locally trivial vector bundle with a connection on a punctured Riemann sphere. Threse exists a construction (called a Deligne construction) of all continuations of vector bundle with a connection to a vector bundle on the hole Riemann sphere with a meromorphic connection. In the talk I'll give a multidimentional generalization of this result. The case when singular divisor has non-normal intersections is also considered.
To obtain such a generalization an algebraic language will be used. The key notion in the construction will be a perverse sheaf.