Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy

Abstract

We present the first explicit examples of a rational threefold and a Calabi-Yau threefold, admitting biregular automorphisms of positive entropy not preserving any dominant rational maps to lower positive dimensional varieties. The most crucial part is the rationality of the quotient threefold of a 3-dimensional torus of product type.

17 pages, no figure, new section 3 (preliminary section for dynamical degrees and relative dynamical degrees for dominant meromorphic maps) is added and several proofs are polished up

References in corpus (2)

• Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces
• Salem numbers in dynamics of Kähler threefolds and complex tori

Cited by in corpus (11)

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• Cylinders in del Pezzo surfaces
• Unirationality of Ueno-Campana's threefold
• Zero entropy automorphisms of compact Kähler manifolds and dynamical filtrations
• On the unirationality of higher dimensional Ueno-type manifolds
• Free abelian group actions on normal projective varieties: sub-maximal dynamical rank case
• Wild automorphisms of projective varieties, the maps which have no invariant proper subsets
• Pseudo-automorphisms with no invariant foliation
• Densities of currents and complex dynamics
• Birational geometry in the study of dynamics of automorphisms and Brody/Mori/Lang hyperbolicity