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arXiv · 1904.09642

A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three

Chen Jiang
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Abstract

We show that there exists a positive real number $\delta>0$ such that for any normal quasi-projective $\mathbb{Q}$-Gorenstein $3$-fold $X$, if $X$ has worse than canonical singularities, that is, the minimal log discrepancy of $X$ is less than $1$, then the minimal log discrepancy of $X$ is not greater than $1-\delta$. As applications, we show that the set of all non-canonical klt Calabi-Yau $3$-folds are bounded modulo flops, and the global indices of all klt Calabi-Yau $3$-folds are bounded from above.

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Chen Jiang. 2019-04-21. A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three. https://doi.org/10.1090/jag%2F759

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