A criterion for the primitivity of a birational automorphism of a Calabi–Yau manifold and an application

We shall give a sufficient condition on the primitivity of a birational automorphism of a Calabi–Yau manifold in purely algebro-geometric terms. As an application, we shall give an explicit construction of Calabi–Yau manifolds of Picard number $2$ of any dimension $\geq 3$, with primitive birational automorphisms of first dynamical degree $\gt 1$.

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The author is supported by JSPS Grant-in-Aid (S) No 25220701, JSPS Grant-in-Aid (S) 15H05738, JSPS Grant-in-Aid (A) 16H02141, JSPS Grant-in-Aid (B) 15H03611, and by KIAS Scholar Program.

Received 4 January 2017

Accepted 14 March 2017

Published 4 June 2018