## Geometry ag.algebraica – On resolution of singularities of Gorenstein

Leave $$(X, o)$$ Being a singularity of Gorenstein isolated, normal, at least. $$3$$. Leave $$pi: widetilde {X} to X$$ be the singularity resolution of $$X$$. Is there a hypersurface? $$H subset X$$ (defined by an equation) such that strict transformation $$widetilde {H}$$ of $$H$$ It is regular and has the property: there is a $$1-1$$-correspondence between the irreducible components of the exceptional divisor of $$widetilde {X}$$ and that of $$widetilde {H}$$?