Universal stacky semistable reduction. (English) Zbl 1467.14005
Summary: Given a log smooth morphism \(f: X \rightarrow S\) of toroidal embeddings, we perform a Raynaud-Gruson type operation on \(f\) to make it flat and with reduced fibers. We do this by studying the geometry of the associated map of cone complexes \(C(X) \rightarrow C(S)\). As a consequence, we show that the toroidal part of semistable reduction of Abramovich-Karu can be done in a canonical way.
MSC:
| 14A20 | Generalizations (algebraic spaces, stacks) |
| 14A21 | Logarithmic algebraic geometry, log schemes |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 14E15 | Global theory and resolution of singularities (algebro-geometric aspects) |
| 14T10 | Foundations of tropical geometry and relations with algebra |
| 14D23 | Stacks and moduli problems |
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