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.

中文翻译：

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通用叠层半稳减

给定环形嵌入的对数光滑态f：X → S，我们对f执行Raynaud-Gruson类型的运算，以使其平坦并具有减少的纤维。我们通过研究圆锥体C（X）→ C（S）的关联图的几何形状来做到这一点。结果，我们证明了Abramovich-Karu的半稳定还原的环形部分可以以规范的方式完成。