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We present the first explicit examples of a rational threefold and aCalabi-Yau threefold, admitting biregular automorphisms of positive entropy notpreserving any dominant rational maps to lower positive dimensional varieties.The most crucial part is the rationality of the quotient threefold of a3-dimensional torus of product type.

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