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

Published online by Cambridge University Press:  12 May 2016

TUYEN TRUNG TRUONG
TUYEN TRUNG TRUONG*
Affiliation:
School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea email [email protected]
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 7 , October 2017 , pp. 2255 - 2275
Copyright
© Cambridge University Press, 2016 

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