A weight-sum condition, called (T), exactly characterizes when the Kirwan blow-up and the toroidal compactification of each of the 85 Deligne-Mostow varieties are naturally isomorphic.
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The Universe of Deligne-Mostow Varieties
A weight-sum condition, called (T), exactly characterizes when the Kirwan blow-up and the toroidal compactification of each of the 85 Deligne-Mostow varieties are naturally isomorphic.