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Factorization for stacks and boundary complexes
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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 $U$.
Forward citations
Cited by 2 Pith papers
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Tropical moduli spaces as symmetric Delta-complexes
Tropical moduli spaces of stable curves are simply connected, Delta_3 is homotopy equivalent to S^5, and Delta_4 has 3-torsion in H_5 and 2-torsion in H_6 and H_7.
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Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks
Compactification independence of the irregular Hodge filtration is proven for Deligne-Mumford stacks, and the resulting orbifold irregular Hodge numbers become invariants of the stacky Landau-Ginzburg model.
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