Relations between indices of Calabi--Yau varieties and pairs

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 $n\ge 3$, any positive integer $m$ satisfying $\phi (m)\le 2n$ can be realized as the index of a klt Calabi--Yau pair of dimension $n-1$.

15 pages

References in corpus (2)

• Complements on log canonical Fano varieties
• Some Results about the Index Conjecture for log Calabi-Yau Pairs

Cited by in corpus (1)

• Smooth Calabi-Yau varieties with large index and Betti numbers