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Jul 14, 2013 at 22:44 comment added HNuer That isn't classically the definition of toroidal varieties. One also requires that the ideal of the boundary restricts locally in these analytic identifications with the toric boundary ideal of the corresponding toric variety. Your definition is that of locally toric varieties, a much weaker and less restrictive class of varieties.
Jun 6, 2013 at 3:33 history asked Li Yutong CC BY-SA 3.0