2 problems

Let $R$ be a regular local ring with a weighted permissible center and consider the associated weighted blow-up with weight vector $(a_1,\ldots,a_n)$, together with strict transfor…

Let $R$ be a regular local ring, let $Z$ be a smooth center, let $S$ be a hypersurface in $R$ containing $Z$, and let $S^+$ be its strict transform under the blow-up of $R$ along…