An Oka Principle for a Parametric Infinite Transitivity Property
An Oka Principle for a Parametric Infinite Transitivity Property
复制标题
参数化无限传递性的奥卡原理
DOI：
10.1007/s12220-016-9749-0
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Alexandre Ramos
中科院分区：
文献类型：
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作者：
F. Kutzschebauch;Alexandre Ramos
全纯自同构的作用是无限传递的，这是一个基本事实，m-传递的。这同样适用于任何具有全纯密度性质X的Stein流形。我们研究一个参数化的情况：我们在由Stein流形W参数化的X上构造点，并寻找由W参数化的X的一族自同构，将它们转化为不依赖于参数的标准形式。一般的传递性是享受奥卡原则，其效果是一个全纯解的障碍是一个纯粹的拓扑性质。在存在体积形式和相应的密度性质的情况下，得到了保体积自同构的类似结果。
It is an elementary fact that the action by holomorphic automorphisms onis infinitely transitive, i.e.,m-transitive for any. The same holds on any Stein manifold with the holomorphic density propertyX. We study a parametrized case: we considermpoints onXparametrized by a Stein manifoldW, and seek a family of automorphisms ofX, parametrized byW, putting them into a standard form which does not depend on the parameter. This general transitivity is shown to enjoy an Oka principle, to the effect that the obstruction to a holomorphic solution is of a purely topological nature. In the presence of a volume form and of a corresponding density property, similar results for volume-preserving automorphisms are obtained.