论文标题
$μ$ $ $ $ $ $ $ $ k稳定性方案的均值计算机
Equivariant calculus on $μ$-character and $μ$K-stability of polarized schemes
论文作者
论文摘要
我们介绍并研究了两极化方案的$ $ k稳定性，就一般测试配置而言是存在的代数几何方面，存在于$μ$ -CSCK指标中，这是在论文Arxiv：1902.00664中引入的，作为统一Kähler-ricci solitons ofKähler-riccicsci sscsck Metrics的框架。本文由两种成分组成。 一方面，我们开发了一个基本框架，涉及“相对模糊相交的衍生物”，我们称之为eproivariant calculus。 e夫剂计算机中的核心主张是某些无限序列的融合结果，这是通过相对epoirivariant交叉点获得的。我们的证明是基于对Derham-Cartan局部有限同源性模型的一些观察结果。该框架提供了一种语言来描述$μ$ k稳定性。我们尤其结论一下，相对于一般测试配置，$μ$ -CSCK歧管的$μ$ k-semistability。 另一方面，我们介绍了一个均等的角色$ \ mathbf {\checkμ}^λ$称为$μ$ - character，用于偏光方案的等效性家族，由$μ$ $ volume-volume功能引入了论文Arxiv1902.00664在Tian-Zhu's partion-khus of theorys k. kath arxiv1902.00664中引入的。 $ $ $ character的衍生品推导了$ $ $ -FUTAKI的一般测试配置不变，此外，它还产生了对等效的CM Line类似CM Line类的类似物的类似物，用于两极分子的cm line bundle for yallocation and yny nes ny $ $ k $ kunbb bunbunibility of Illocatation of Ilaligation of Iltalliate and $ \ bunbbieny noutibility n unive nou n unive nous $ \ bunb c} Q} Q} 设置。
We introduce and study $μ$K-stability of polarized schemes with respect to general test configurations as an algebro-geometric aspect of the existence of $μ$-cscK metrics, which is introduced in the paper arXiv:1902.00664 as a framework unifying the frameworks of Kähler-Ricci solitons and cscK metrics. This article consists of two ingredients. On one hand, we develop a foundational framework concerning `derivative of relative equivariant intersection', which we call equivariant calculus. A core claim in equivariant calculus is a convergence result for some infinite series in equivariant cohomology, which is obtained by relative equivariant intersections. Our proof is based on some observations on deRham-Cartan model of equivariant locally finite homology. This framework furnishes a language to describe $μ$K-stability. We in particular conclude the $μ$K-semistability of $μ$-cscK manifolds with respect to general test configurations. On the other hand, we introduce an equivariant character $\mathbf{\checkμ}^λ$ called $μ$-character for equivariant family of polarized schemes, motivated by the $μ$-volume functional introduced in the paper arXiv1902.00664 as a generalization of Tian-Zhu's functional in the theory of Kähler-Ricci soliton. The equivariant derivative of the $μ$-character derive $μ$-Futaki invariant for general test configuration, and furthermore, it also produces an analogue of the equivariant first Chern class of CM line bundle for family of polarized schemes, which is irrational and hence cannot be realized as a $\mathbb{Q}$-line bundle in our general $μ$K-stability setup.
