On endomorphisms of arrangement complements
On endomorphisms of arrangement complements
Let $\Omega$ be the complement of a connected, essential hyperplane arrangement. We prove that every dominant endomorphism of $\Omega$ extends to an endomorphism of the tropical compactification $X$ of $\Omega$ associated to the Bergman fan structure on the tropical variety $\operatorname {trop}(\Omega )$. This generalizes a result in [Compos. Math. …