95 citations · 531 across the 39 of their papers we have counts for
39 papers
Stable degenerations of singularities
Chenyang Xu, Ziquan Zhuang
For any Kawamata log terminal (klt) singularity and any minimizer of its normalized volume function, we prove that the associated graded ring is always finitely generated, as conje…
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…
Uniqueness of the minimizer of the normalized volume function
Chenyang Xu, Ziquan Zhuang
We confirm a conjecture of Chi Li which says that the minimizer of the normalized volume function for a klt singularity is unique up to rescaling. This is achieved by defining stab…
Openness of K-semistability for Fano varieties
Harold Blum, Yuchen Liu, Chenyang Xu
In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also pro…
A Minimizing Valuation is Quasi-monomial
Chenyang Xu
We prove a version of Jonsson-Mustaţǎ's Conjecture, which says for any graded sequence of ideals, there exists a quasi-monomial valuation computing its log canonical threshold. As…
Moduli of polarized Calabi-Yau pairs
János Kollár, Chenyang Xu
We prove that the irreducible components of the moduli space of polarized Calabi-Yau pairs are projective.