Arithmetic degrees for dynamical systems over function fields of characteristic zero
Arithmetic degrees for dynamical systems over function fields of characteristic zero
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DOI：
10.1007/s00209-018-2053-x
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发表时间：
2017-01
影响因子：
0.8
通讯作者：
Yohsuke Matsuzawa;K. Sano;Takahiro Shibata
中科院分区：
文献类型：
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作者：
Yohsuke Matsuzawa;K. Sano;Takahiro Shibata
研究了特征为零的函数域上光滑射影变上的占优有理自映射的算术度。从几何角度解释了算术度的概念，研究了函数域上的相关问题。对任意点的算术次小于等于动态次的定理，给出了另一个证明。提出了算术度与动态度重合的一个充分条件，并证明了任意自映射都有许多算术度等于动态度的点。我们还详细研究了射影空间上的占优理性自映射。
We study the arithmetic degree of a dominant rational self-map on a smooth projective variety over a function field of characteristic zero. We interpret the notion of arithmetic degree and study related problems over function fields geometrically. We give another proof of the theorem that the arithmetic degree at any point is smaller than or equal to the dynamical degree. We also suggest a sufficient condition for the arithmetic degree to coincide with the dynamical degree, and prove that any self-map has many points whose arithmetic degrees are equal to the dynamical degree. We also study dominant rational self-maps on projective spaces in detail.