7 citations · 9 across the 2 of their papers we have counts for
8 papers
On properness of K-moduli spaces and optimal degenerations of Fano varieties
Harold Blum, Daniel Halpern-Leistner, Yuchen Liu +1
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…
Equivariant K-stability under finite group action
Yuchen Liu, Ziwen Zhu
We show that G-equivariant K-semistability (resp. G-equivariant K-polystability) implies K-semistability (resp. K-polystability) for log Fano pairs when G is a finite group.
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.
Stability conditions on product varieties
Yucheng Liu
Given a stability condition on a smooth projective variety , we construct a family of stability conditions on , where is a smooth projective curve. In particular,…
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…
Openness of uniform K-stability in families of -Fano varieties
Harold Blum, Yuchen Liu
We show that uniform K-stability is a Zariski open condition in Q-Gorenstein families of Q-Fano varieties. To prove this result, we consider the behavior of the stability threshold…