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

Original · EN

Let X₀ be a smooth projective threefold which is Fano or which has Picard number 1. Let π:X→ X₀ be a finite composition of blowups along smooth centers. We show that for "almost all" of such X, if f∈ Aut(X) then its first and second dynamical degrees are the same. We also construct many examples of finite blowups X→ X₀, on which any automorphism is of zero entropy. The main idea is that because of the log-concavity of dynamical systems 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.