# Example of height $n$ ideal with $I/I^2$ (locally) $n$-generated, but $I$ is not.

For $R$, a commutative noetherian ring of dimension $d$, I'm looking for an example where $I \subset R$ is an ideal of height $n \lt d$ such that $I/I^2$ is generated by $n$ elements (locally $n$-generated is also fine), however, $I$ itself is not. Moreover, it would be greatly helpful if your response could address the geometric intuition of the example as well.

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