2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210615We study the local geometry of the pullback of a variety via a finite holomorphic map. In particular, we are looking for properties of $V = F^{-1}(W)$ such that if $V$ has the property $A$, then $W$ must have the property $A$. We show that $A$ can be the property of normality or prefactoriality. We also show that $A$ can be the property of smoothness, under extra assumptions.8 pages, latexComplex VariablesAlgebraic Geometry32B10; 32H02; 14B99text