论文标题
加权K稳定性$ \ MATHBB Q $ -FANO球形品种
Weighted K-stability of $\mathbb Q$-Fano spherical varieties
论文作者
论文摘要
让$ g $为连接的，复杂的还原谎言组，$ x $ a $ \ m马布Q $ -Fano $ g $ - $ spherical varret。在本文中，我们通过组合数据计算了$ g $ equivariant的普通测试配置的称重的非Archimedean功能。同样，我们对重量$ g $定义了修改的Futaki不变，并在交叉数字方面表达了一种表达。最后，我们展示了稳定性不同的等值表示，并在$ \ mathbb Q $ -Fano球形品种上给出了稳定性标准，这也是Kähler-ricci $ g $ solitons存在的标准。
Let $G$ be a connected, complex reductive Lie group and $X$ a $\mathbb Q$-Fano $G$-spherical variety. In this paper we compute the weighed non-Archimedean functionals of a $G$-equivariant normal test configurations of $X$ via combinatory data. Also we define a modified Futaki invariant with respect to the weight $g$, and give an expression in terms of intersection numbers. Finally we show the equivalence of different notations of stability and gives a stability criterion on $\mathbb Q$-Fano spherical varieties, which is also a criterion of existence of Kähler-Ricci $g$-solitons.
