Let $X$ be an reduced and irreducible complex analytic space of dimension $m$ and $Z$ an $n$-dimensional irreducible analytic subset of $X$ with reduced structure.
Then we say that $Z$ locally complete intersect at $x\in Z$ if there exists an open neighborhood $U_x$ of $x$ in $X$ such that the ideal sheaf $\mathcal{I}_Z$ is generated by a regular sequence of length $m-n$ on $U_x$. (Note: This condition may be equivalent to $\mathcal{I}_{Z,x}$ being generated by a regular sequence of length $m-n$.)
Question: Is $Z$ locally complete intersects at the general point of $Z$? (general points means $Z$ minus some proper analytic subset of $Z$)
One can freely impose conditions to discuss this issue. Any comments and clues will be appreciated.