37 citations · 362 across the 39 of their papers we have counts for
7 papers · 1 filter
ACC for local volumes and boundedness of singularities
Jingjun Han, Yuchen Liu, Lu Qi
The ACC conjecture for local volumes predicts that the set of local volumes of klt singularities satisfies the ACC if the coefficients of belong to a DCC set. In t…
On K-stability of some del Pezzo surfaces of Fano index 2
Yuchen Liu, Andrea Petracci
For every integer , we relate the K-stability of hypersurfaces in the weighted projective space of degree with the GIT stability of binary form…
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…
Some quadratic inequalities on product varieties
Yucheng Liu
We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability c…
K-stability of cubic fourfolds
Yuchen Liu
We prove that the K-moduli space of cubic fourfolds is identical to their GIT moduli space. More precisely, the K-(semi/poly)stability of cubic fourfolds coincide to the correspond…
K-moduli of curves on a quadric surface and K3 surfaces
Kenneth Ascher, Kristin DeVleming, Yuchen Liu
We show that the K-moduli spaces of log Fano pairs where is a -curve and their wall crossings coincide with the VGIT quotients of…
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.