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Some Examples of Calabi–Yau Pairs with Maximal Intersection and No Toric Model

Some Examples of Calabi–Yau Pairs with Maximal Intersection and No Toric Model

It is known that a maximal intersection log canonical Calabi–Yau surface pair is crepant birational to a toric pair. This does not hold in higher dimension: this article presents some examples of maximal intersection Calabi–Yau pairs that admit no toric model.