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Automorphisms of blowups of threefolds being Fano or having Picard number 1


Let $X_{0}$ be a smooth projective threefold which is Fano or which has Picard number 1. Let $\unicode[STIX]{x1D70B}:X\rightarrow X_{0}$ be a finite composition of blowups along smooth centers. We show that for ‘almost all’ of such $X$ , if $f\in \text{Aut}(X)$ , then its first and second dynamical degrees are the same. We also construct many examples of blowups $X\rightarrow X_{0}$ , on which any automorphism is of zero entropy. The main idea is that, because of the log-concavity of dynamical degrees and the invariance of Chern classes under holomorphic automorphisms, there are some constraints on the nef cohomology classes. We will also discuss a possible application of these results to a threefold constructed by Kenji Ueno.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
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