论文标题
两极化品种的加权K稳定性和Sasaki歧管的极端性
Weighted K-stability of polarized varieties and extremality of Sasaki manifolds
论文作者
论文摘要
我们使用极端的Sasaki结构与加权的极值Kahler指标，该指标定义为前两位作者建立的Sasaki歧管的常规商，以及Lahdili的加权K稳定性理论，以定义（相对）加权K稳定性的常规类型的（相对）加权k稳定性的概念。我们表明，（相对）加权K稳定性相对于最大圆环是存在（可能是不规则的）极端Sasaki度量的必要条件。我们还将加权K稳定性与相应的极化仿射锥（由Collins-SzekelyHidi引入）的K稳定性进行了比较，并证明他们同意我们考虑的测试配置类别。作为副产品，我们加强了对标量 - 平台Kahler锥指标的存在的障碍，从k-易理解性到这些测试构型的K稳定性。我们使用我们的方法来表征兼容的极值Sasaki结构在主圆束上，这是在可允许的统治歧管上的，它是根据给定间隔的一个多项式的单个多项式的阳性表示的。
We use the correspondence between extremal Sasaki structures and weighted extremal Kahler metrics defined on a regular quotient of a Sasaki manifold, established by the first two authors, and Lahdili's theory of weighted K-stability in order to define a suitable notion of (relative) weighted K-stability for compact Sasaki manifolds of regular type. We show that the (relative) weighted K-stability with respect to a maximal torus is a necessary condition for the existence of a (possibly irregular) extremal Sasaki metric. We also compare weighted K-stability to the K-stability of the corresponding polarized affine cone (introduced by Collins-Szekelyhidi), and prove that they agree on the class of test configurations we consider. As a byproduct, we strengthen the obstruction to the existence of a scalar-flat Kahler cone metric from the K-semistability to the K-stability on these test configurations. We use our approach to give a characterization of the existence of a compatible extremal Sasaki structure on a principal circle bundle over an admissible ruled manifold, expressed in terms of the positivity of a single polynomial of one variable over a given interval.
