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Let $X$ be a projective variety defined over an infinite field, equipped witha line bundle $L$, giving an embedding of $X$ into $\mb{P}^m$ and let $\phi: X\to X$ be a morphism such that $\phi^*L \cong L^{\otimes q}, q\geq 2$. Thenthere exists an integer $r>0$ extending $\phi^r$ to $\mb{P}^m$.

Very ample polarized self maps extend to projective space