论文标题
理性表面自动形态的动态程度
The Dynamical Degrees of Rational Surface Automorphisms
论文作者
论文摘要
可以用与$ e_n，n \ ge 10 $图相关的Coxeter组的元素来识别对带正熵的Picard组的诱导作用。因此，理性表面自动形态的动态程度集是Coxeter组元素光谱半径的子集。本文涉及Coxeter组的一个元素作为理性表面上具有不可还原抗典型曲线的自动形态。对于任何无法实现的元素，我们明确构建具有相同光谱半径的可实现元素。因此，我们表明，Coxeter组的动力学程度和光谱半径集实际上是相同的。 uehara在\ cite {uehara：2010}中已通过明确构建有理表面自动形态来表明这一点。该结构取决于Coxeter组元素的分解。我们的证明是概念性的，并简单地描述了Coxeter群体的元素，这是由自动形态在反典型理性表面上实现的。
The induced action on the Picard group of a rational surface automorphism with positive entropy can be identified with an element of the Coxeter group associated to $E_n, n\ge 10$ diagram. It follows that the set of dynamical degrees of rational surface automorphisms is a subset of the spectral radii of elements in the Coxeter group. This article concerns the realizability of an element of the Coxeter group as an automorphism on a rational surface with an irreducible reduced anti-canonical curve. For any unrealizable element, we explicitly construct a realizable element with the same spectral radius. Hence, we show that the set of dynamical degrees and the set of spectral radii of the Coxeter group are, in fact, identical. This has been shown by Uehara in \cite{Uehara:2010} by explicitly constructing a rational surface automorphism. This construction depends on a decomposition of an element of the Coxeter group. Our proof is conceptual and provides a simple description of elements of the Coxeter group, which are realized by automorphisms on anti-canonical rational surfaces.
