Liu's minimal mld conjecture for standard-coefficient Calabi-Yau pairs

Let nn be a positive integer, and let (X,D)(X,D) be the explicitly constructed klt Calabi-Yau pair in dimension nn with standard coefficients, namely the pair defined by the source's displayed construction. Its minimal log discrepancy is

1sn+11.\frac{1}{s_{n+1}-1}.

Liu's minimal mld conjecture. The number 1/(sn+11)1/(s_{n+1}-1) is the smallest possible minimal log discrepancy among all nn-dimensional klt Calabi-Yau pairs with standard coefficients.

The claim proposes that Liu's example is extremal for minimal log discrepancies in this class. The source gives no resolution status.

Sources & referencesView supporting material

Primary source

Louis Esser, Burt Totaro and Chengxi Wang, “Calabi-Yau varieties of large index”, arXiv:2209.04597 (2022).

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