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Factorization for stacks and boundary complexes (1706.07999v1)
Published 24 Jun 2017 in math.AG
Abstract: We prove a weak factorization result on birational maps of Deligne-Mumford stacks, and deduce the following: Let $U \subset X$ be an open embedding of smooth Deligne-Mumford stacks such that $D = X-U$ is a normal crossings divisor, then the the simple homotopy type of the boundary complex $\Delta(X,D)$ depends only on $U$.