Let $P,Q\subset\mathbb{R}^n$ lattice polytopes such that $P$ and $P'=P+Q$ are smooth polytopes. We obtain the birational morphism $f:X_{P'}\to X_Q$ and I am interested in a criterion when this is a resolution of singularities. Since $X_{P'}$ is smooth, we only need to check whether $f$ is an isomorphism away from the singularieties of $X_Q$. Can we phrase this nicely in terms of the lattice polytopes $P$ and $Q$?
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