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If $RI_2$ is a height one idealgenerated by $n$ quadrics, then $I_2 \\subset (w)$ after a possible change of variables. Let $J = I \\cap k[x_1,..., x_n]$. Then $\\mu(I) \\le \\mu(J)+n+1$ and $I$ is said to be generic if $\\mu(I) = \\mu(J) + n+1$. In this article we prove necessary conditions, in terms of $F$, for an ideal to be generic. 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