On the Jacobian ring of a complete intersection

Let f1,…,fr∈K[x], K is a field, be homogeneous polynomials and put . The quotient J=K[x,y]/I, where I is the ideal generated by the ∂F/∂xi and ∂F/∂yj, is the Jacobian ring of F. We describe J by computing the cohomology of a certain complex whose top cohomology group is J.