论文标题
复杂性动作的纳什问题一个
The Nash problem for torus actions of complexity one
论文作者
论文摘要
我们解决了任何非理性的正常品种，并解决了复杂性的动作。也就是说，我们在任何此类品种上对NASH顺序进行了明确的组合描述。使用此描述，我们在这种情况下积极解决了经典的NASH问题，表明每个基本估值都是NASH估值。我们还描述了终端估值，并利用我们的结果来负面回答蕨类植物和docampo的问题，构建既不是最小也不是终端的纳什估值的例子，从而说明了正在考虑的奇异之类的奇异级别的新特征。
We solve the equivariant generalized Nash problem for any non-rational normal variety with torus action of complexity one. Namely, we give an explicit combinatorial description of the Nash order on the set of equivariant divisorial valuations on any such variety. Using this description, we positively solve the classical Nash problem in this setting, showing that every essential valuation is a Nash valuation. We also describe terminal valuations and use our results to answer negatively a question of de Fernex and Docampo by constructing examples of Nash valuations which are neither minimal nor terminal, thus illustrating a striking new feature of the class of singularities under consideration.
