Automorphisms of blowups of threefolds being Fano or having Picard number 1
Automorphisms of blowups of threefolds being Fano or having Picard number 1
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三倍放大的自同构为 Fano 或具有 Picard 数 1
DOI：
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发表时间：
2015
影响因子：
0.9
通讯作者：
T. Truong
中科院分区：
文献类型：
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作者：
T. Truong
设$X_{0}$是Fano或Picard数为1的三重光滑射影.设$Unicode[stix]{x1D70B}：x
右行X_{0}$是沿光滑中心的鼓包的有限合成。我们证明了对于几乎所有这样的$X$，如果$Fin Ext{Aut}(X)$，则它的第一和第二动力学次数是相同的。我们还构造了许多放大$X的例子
右行X_{0}$，其上的任何自同构为零熵。其主要思想是，由于动态度的对数凹性和Chern类在全纯自同构下的不变性，对nef上同调类有一定的约束。我们还将讨论这些结果在上野健二构造的三重数中的可能应用。
Let $X_{0}$ be a smooth projective threefold which is Fano or which has Picard number 1. Let $unicode[STIX]{x1D70B}:X
ightarrow X_{0}$ be a finite composition of blowups along smooth centers. We show that for ‘almost all’ of such $X$ , if $fin ext{Aut}(X)$ , then its first and second dynamical degrees are the same. We also construct many examples of blowups $X
ightarrow X_{0}$ , 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.