论文标题
在Kawaguchi-silverman猜想中，构成了不规则品种的男子式汽车
On the Kawaguchi--Silverman Conjecture for birational automorphisms of irregular varieties
论文作者
论文摘要
我们研究了Kawaguchi-Silverman的主要开放部分，并断言，对于平稳的投射型$ x $的男子式自动图$ f $，定义在$ \ operline {\ Mathbb Q} $上，算术$ $ $α_f（x）$存在，并与任何动态学$ $Δ_f$ copert $ unive $ cy-c coptline- $ x $ $ x $，带有Zariski密集轨道。除其他结果外，我们还表明，当$ x $具有kodaira dimension零和不规则性$ q（x）\ ge \ dim x -1 $或$ x $是不规则的三倍（modulo一个可能的例外）时，这将成立。我们还研究了Zariski致密轨道的存在，并具有明确的例子。
We study the main open parts of the Kawaguchi--Silverman Conjecture, asserting that for a birational self-map $f$ of a smooth projective variety $X$ defined over $\overline{\mathbb Q}$, the arithmetic degree $α_f(x)$ exists and coincides with the first dynamical degree $δ_f$ for any $\overline{\mathbb Q}$-point $x$ of $X$ with a Zariski dense orbit. Among other results, we show that this holds when $X$ has Kodaira dimension zero and irregularity $q(X) \ge \dim X -1$ or $X$ is an irregular threefold (modulo one possible exception). We also study the existence of Zariski dense orbits, with explicit examples.
