Explicit Examples of Rational and Calabi-Yau Threefolds with Primitive Automorphisms of Positive Entropy

J. Math. Sci. Univ. Tokyo
Vol. 22 (2015), No. 1, Page 361–385.

Oguiso, Keiji ; Truong, Tuyen Trung
Explicit Examples of Rational and Calabi-Yau Threefolds with Primitive Automorphisms of Positive Entropy
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

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. These examples are also the first whose dynamical degrees are not Salem numbers. Crucial parts are the rationality of the quotient threefold of a certain $3$-dimensional torus of product type and a numerical criterion of primitivity of birational automorphisms in terms of dynamical degrees.

Keywords: Rationality of manifolds, rational threefold, Calabi-Yau threefold, primitive automorphism, entropy, dynamical degrees.

Mathematics Subject Classification (2010): 14E08, 14J32, 14J50, 37F99.
Mathematical Reviews Number: MR3329200

Received: 2014-07-07