Given a log smooth morphism f: X → 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) → C(S). As a consequence, we show that the toroidal part of semistable reduction of Abramovich-Karu can be done in a canonical way.
Universal Stacky Semistable Reduction / Molcho, S. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - (2021). [10.1007/s11856-021-2118-0]
Universal Stacky Semistable Reduction
Molcho S
2021
Abstract
Given a log smooth morphism f: X → 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) → C(S). As a consequence, we show that the toroidal part of semistable reduction of Abramovich-Karu can be done in a canonical way.File allegati a questo prodotto
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