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

TL;DR

This paper establishes a purely algebraic criterion for the primitivity of birational automorphisms on Calabi-Yau manifolds and constructs examples of such manifolds with primitive automorphisms of high dynamical degree.

Contribution

It provides a new algebraic condition for primitivity and explicitly constructs Calabi-Yau manifolds with primitive automorphisms of Picard number 2 in dimensions ≥3.

Findings

Criterion for primitivity of birational automorphisms

Explicit construction of Calabi-Yau manifolds with primitive automorphisms

Existence of automorphisms with dynamical degree > 1

Abstract

We shall give a sufficient condition on the primitivity of a birational automrphism 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 $\ge 3$, with primitive birational automrphisms of first dynamical degree $>1$.