Let V be a analytic set of $C^n$, $I(V)$ is the sheaf of ideals of V (the sheaf whose stalks are ideals defining germs of V at its points). Since $I(V)$ is a coherent analytic sheaf, we see that in a neighborhood D of a point p of V there are holomorphic function $g_1,g_2,\ldots,g_t$ such that $V\cap D=$ {$g_1=g_2=\cdots=g_t=0$}. Let $k=\dim_p V$.

If p is a regular point of V, evidently we can choose $t=n-k$.

If V is hypersurface we can choose $t=1=n-k$.

My question is: in general, can we choose $t=n-k$, or equivalently, an analytic is locally intersection of (n-k) hypersurface?