On the Jacobian ring of a complete intersection
Abstract
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.
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