论文标题
最小化CM学位和特别的K型品种
Minimizing CM degree and specially K-stable varieties
论文作者
论文摘要
We prove that the degree of the CM line bundle for a normal family over a curve with fixed general fibers is strictly minimized if the special fiber is either a smooth projective manifold with a unique cscK metric or ``specially K-stable", which is a new class we introduce in this paper. This phenomenon, as conjectured by Odaka (cf., [Oda20]), is a quantitative strengthening of the separatedness极化K稳定品种的模量空间的猜想。 上面提到的特殊K稳定性意味着原始的K稳定性，并且很多情况都满足，例如K-Stable Log Fano，Klt Calabi-yau（即$ k_x \ equiv0 $），LC品种具有足够的规范性分区，均匀绝对绝对绝能klt klt klt-klt-triv hat-triv-trivial fibrations（Cocf.）
We prove that the degree of the CM line bundle for a normal family over a curve with fixed general fibers is strictly minimized if the special fiber is either a smooth projective manifold with a unique cscK metric or ``specially K-stable", which is a new class we introduce in this paper. This phenomenon, as conjectured by Odaka (cf., [Oda20]), is a quantitative strengthening of the separatedness conjecture of moduli spaces of polarized K-stable varieties. The above mentioned special K-stability implies the original K-stability and a lot of cases satisfy it e.g., K-stable log Fano, klt Calabi-Yau (i.e., $K_X\equiv0$), lc varieties with the ample canonical divisor and uniformly adiabatically K-stable klt-trivial fibrations over curves (cf., [Hat22]).
