论文标题
大型自动形态群的投影表面的肥大性
Hyperbolicity for large automorphism groups of projective surfaces
论文作者
论文摘要
我们研究了非元素自构基团在紧凑的复合表面上的作用的双曲度特性，重点是K3并富集表面。第一个结果是，当这样的组包含抛物线元素时，Zariski扩散不变的度量会自动具有非零的lyapunov指数。结合我们以前的工作，这导致了整个表面上均匀扩展特性的简单标准，对于有和没有抛物线元素的群体。反过来，这对动态产生了强烈的后果：轨道封闭，等均分布，千古特性等的描述等。 在此过程中，我们提供了有关非线性离散组动作在紧凑型（真实）歧管上的均匀扩展以及在最佳力矩条件下构建Margulis功能的参考讨论。
We study the hyperbolicity properties of the action of a non-elementary automorphism group on a compact complex surface, with an emphasis on K3 and Enriques surfaces. A first result is that when such a group contains parabolic elements, Zariski diffuse invariant measures automatically have non-zero Lyapunov exponents. In combination with our previous work, this leads to simple criteria for a uniform expansion property on the whole surface, for groups with and without parabolic elements. This, in turn, has strong consequences on the dynamics: description of orbit closures, equidistribution, ergodicity properties, etc. Along the way, we provide a reference discussion on uniform expansion of non-linear discrete group actions on compact (real) manifolds and the construction of Margulis functions under optimal moment conditions.
