Let $(X,o)$ be an isolated, normal singularity of dimension at least $3$. Let $\pi: \widetilde{X} \to X$ be a resolution of singularity of $X$. Is it true that for a general hypersurface $H \subset X$ (defined by one equation) passing through $o$, the strict tranform $\widetilde{H}$ of $H$ is regular?
$\begingroup$
$\endgroup$
Add a comment
|