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arXiv · 1309.3695

Pseudo-automorphisms with no invariant foliation

Eric Bedford·Serge Cantat·Kyounghee Kim
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Abstract

We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are $>1$, but which does not preserve any holomorphic (singular) foliation. In particular, this provides a negative answer to a question of Guedj. On our way, we develop several techniques to study foliations which are invariant under birational transformations.

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Eric Bedford, Serge Cantat, Kyounghee Kim. 2013-09-14. Pseudo-automorphisms with no invariant foliation. https://arxiv.org/abs/1309.3695

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