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Pseudo-automorphisms with no invariant foliation

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  • 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.
    Mathematics Subject Classification: Primary: 37F10; Secondary: 32H50, 14E07.

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