 the set of ${\boldsymbol}{x} \in V(R_0^{d_0},\ldots,R_m^{d_m})$ for which $(\partial {\boldsymbol}{R}^{{\boldsymbol}{d}}/\partial {\boldsymbol}{X})({\boldsymbol}{x})$ has not full rank, has codimension at least 0 in $V(R_0^{d_0}{\ifm {,\ldots,} {$,\ldots,$}}R_m^{d_m})$. Then Theorem \[theorem: eisenbud 00.00\] proves that $R_0^{