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arXiv · 2312.16077

Relations between indices of Calabi--Yau varieties and pairs

Yuto Masamura
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Abstract

We show that for any smooth Calabi--Yau variety, its index can be realized as the index of a Kawamata log terminal (klt) Calabi--Yau pair of lower dimension with standard coefficients. Our approach is based on an inductive argument on the dimension using the Beauville--Bogomolov decomposition. A key step in the argument is to prove that for $n\ge3$, any positive integer $m$ satisfying $\varphi(m)\le 2n$ can be realized as the index of a klt Calabi--Yau pair of dimension $n-1$.

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Yuto Masamura. 2023-12-26. Relations between indices of Calabi--Yau varieties and pairs. https://doi.org/10.1093/imrn%2Frnaf114

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