A log resolution of \(X\) is a proper birational morphism \(h: Y \rightarrow X\) from a non-singular variety \(Y\), which is an isomorphism outside \(h^{-1}(D)\) and such that \(h^{-1}(D)\) a strict normal crossings divisor - i.e. the irreducible components of \(h^{-1}(\operatorname{Supp} D)\), denoted by \(\left\{E_{i}\right\}_{i \in J}\), are smooth and intersect each other transversally).