63 citations · 275 across the 28 of their papers we have counts for
6 papers · 1 filter
On positivity of the CM line bundle on K-moduli spaces
Chenyang Xu, Ziquan Zhuang
In this paper, we consider the CM line bundle on the K-moduli space, i.e., the moduli space parametrizing K-polystable Fano varieties. We prove it is ample on any proper subspace p…
Some criteria for uniform K-stability
Chuyu Zhou, Ziquan Zhuang
We prove some criteria for uniform K-stability of log Fano pairs. In particular, we show that uniform K-stability is equivalent to -invariant having a positive lower bound. Then…
On the Cheltsov--Rubinstein conjecture
Kento Fujita, Yuchen Liu, Hendrik Süß +2
In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.
Product theorem for K-stability
Ziquan Zhuang
We prove a product formula for -invariant and as an application, we show that product of K-(semi, poly)stable Fano varieties is also K-(semi, poly)stable.
On the sharpness of Tian's criterion for K-stability
Yuchen Liu, Ziquan Zhuang
Tian's criterion for K-stability states that a Fano variety of dimension whose alpha invariant is greater than is K-stable. We show that this criterion is sharp…
Birational superrigidity is not a locally closed property
Ziquan Zhuang
We prove an optimal result on the birational rigidity and K-stability of index hypersurfaces in with ordinary singularities when and also study the…