On the structure of the endomorphism ring of a certain local cohomology module

Let (R,m) denote an n-dimensional Gorenstein ring. For an ideal I⊂R of height c we are interested in the endomorphism ring . It turns out that B is a commutative ring. In the case of (R,m) a regular local ring containing a field B is a Cohen–Macaulay ring. Its properties are related to the highest Lyubeznik number , . In particular R≃B if and only if l=1. Moreover, we show that the natural homomorphism is non-zero.