On the Jacobian ring of a complete intersection

الأصل · EN

Let f₁,...,fᵣ be homogeneous polynomials in K[x₁,...,xₙ], K a field. Put F=y₁f₁+...+yᵣfᵣ in K[x,y] and let I be the ideal of K[x,y] generated by the partials of F relative to the xᵢ and yⱼ. The Jacobian ring of F is the quotient J:=K[x,y]/I. We describe J by computing the cohomology of a certain complex whose top cohomology group is J.