Corollary 9.3.6522466FA1EC1

Corollary 9.3.6.522466FA1EC1 Let $(A,0)\subset (\mathbb C^ n,0)$ be an irreducible analytic germ, and let $(B,0)$ be an analytic subgerm different from $(A,0)$. Let $\Delta '\times \Delta ''$ be a parametrization polydisc of $(A,0)$ as in theorem 9.3.4, with its representative $A$ and covering locus $A_\delta $, so small that $(B,0)$ has a representative $B$ which is an analytic subset of $\Delta '\times \Delta ''$. Then $A_\delta \setminus B$ is dense in $A\cap (\Delta '\times \Delta '')$. In particular, $(A\cap (\Delta '\times \Delta ''))\setminus B$ is dense in $A\cap (\Delta '\times \Delta '')$, and so is the regular locus of $A\cap (\Delta '\times \Delta '')$, which contains $A_\delta $.