Factorization for stacks and boundary complexes

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 $U$.

21 pages, comments are welcome

References in corpus (3)

• The tropicalization of the moduli space of curves
• Desingularization of quasi-excellent schemes in characteristic zero
• Presenting higher stacks as simplicial schemes

Cited by in corpus (6)

• Tropical curves, graph complexes, and top weight cohomology of M_g
• Topology of moduli spaces of tropical curves with marked points
• Tropical moduli spaces as symmetric Delta-complexes
• Functorial destackification and weak factorization of orbifolds
• Weak factorization and the Grothendieck group of Deligne-Mumford stacks
• Automorphisms of tropical Hassett spaces