论文标题
代数品种和无限传递性的自动形态
Automorphisms of algebraic varieties and infinite transitivity
论文作者
论文摘要
我们调查了有关仿射代数品种的自动形态群体多种传递性的最新结果。我们考虑特殊自多态群的无限传递性的特性，这相当于相应的仿射品种的柔韧性。这些特性具有重要的代数和几何后果。同时，它们适用于各种品种。同样，我们还研究了有限的许多参数亚组产生的自动形态群体发生无限传递率的情况。在本文的附录中，讨论了复杂分析和组合群体理论中无限传递作用的结果。
We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the corresponding affine variety. These properties have important algebraic and geometric consequences. At the same time they are fulfilled for wide classes of varieties. Also we study situations where infinite transitivity takes place for automorphism groups generated by finitely many one-parameter subgroups. In the appendices to the paper, the results on infinitely transitive actions in complex analysis and in combinatorial group theory are discussed.
