论文标题
关于K-Moduli空间的正常和Fano品种的最佳变性
On properness of K-moduli spaces and optimal degenerations of Fano varieties
论文作者
论文摘要
我们建立了一种代数方法，以证明K-Polystable Fano品种的模量空间的适当性，并将问题减少到对K- Unstable Fano品种不稳定的猜想。具体而言，我们证明，如果每个K- Unstable Fano品种的稳定性阈值都是通过分区估值计算的，那么此类K-Moduli空间是正确的。该论点依赖于研究某些最佳的不稳定测试构型，并在Fano品种的模量堆栈上构建theta分离。
We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties. Specifically, we prove that if the stability threshold of every K-unstable Fano variety is computed by a divisorial valuation, then such K-moduli spaces are proper. The argument relies on studying certain optimal destabilizing test configurations and constructing a Theta-stratification on the moduli stack of Fano varieties.
