论文标题
在Yau-Tian-Donaldson的猜想中
On the Yau-Tian-Donaldson conjecture for generalized Kähler-Ricci soliton equations
论文作者
论文摘要
令$（x，d）$是具有有效holomorphic torus Action的原木品种，而$θ$为封闭的正$（1,1）$ - 当前。对于在圆环动作的瞬间矩元素上定义的任何平稳的正函数$ g $，我们研究了对应于广义和扭曲的kähler-ricci $ g $ solitons的蒙格 - 安培方程。我们证明了这些通用方程式的Yau-Tian-Donaldson（YTD）猜想的版本，这表明解决方案的存在始终等于等效统一的$θ$ twist $ twist $ g $ g $ ding-ding稳定性。当$θ$是与圆环不变的线性系统相关的电流时，我们进一步表明，等效的特殊测试配置足以测试稳定性。我们的结果允许任意KLT奇异性，并将大多数先前的结果推广到（均匀）YTD猜想的（扭曲）Kähler-ricci/mabuchi solitons或Kähler-Einstein指标上。
Let $(X, D)$ be a log variety with an effective holomorphic torus action, and $Θ$ be a closed positive $(1,1)$-current. For any smooth positive function $g$ defined on the moment polytope of the torus action, we study the Monge-Ampère equations that correspond to generalized and twisted Kähler-Ricci $g$-solitons. We prove a version of Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing that the existence of solutions is always equivalent to an equivariantly uniform $Θ$-twisted $g$-Ding-stability. When $Θ$ is a current associated to a torus invariant linear system, we further show that equivariant special test configurations suffice for testing the stability. Our results allow arbitrary klt singularities and generalize most of previous results on (uniform) YTD conjecture for (twisted) Kähler-Ricci/Mabuchi solitons or Kähler-Einstein metrics.
