Semi-log canonical varieties are a higher-dimensional analogue of stable curves. They are the varieties appearing as the boundary $\Delta $ of a log canonical pair $(X,\Delta )$ and also appear as limits of canonically polarized varieties in moduli theory. For certain three-fold pairs $(X,\Delta ),$ we show how to compute the PL homeomorphism type of the dual complex of a dlt minimal model directly from the normalization data of $\Delta $.

中文翻译：

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半对数规范曲面的对偶复形

半对数规范变体是稳定曲线的高维模拟。它们是作为对数规范对 $(X,\Delta )$ 的边界 $\Delta $ 出现的簇，并且在模理论中也作为规范极化簇的极限出现。对于某些三重对 $(X,\Delta ),$，我们展示了如何直接从 $\Delta $ 的归一化数据计算 dlt 最小模型的对偶复形的 PL 同胚类型。