14 citations · 24 across the 11 of their papers we have counts for
29 papers
Stable Degeneration, Non-degenerate Forms, and Kaledin's Conjecture
Chenyang Xu, Ziquan Zhuang, Henri Guenancia
We prove that stable degeneration, the canonical degeneration associated to the normalized volume minimizer of a Kawamata log terminal (klt) singularity, preserves non-degenerate r…
Open problems in K-stability of Fano varieties
Chenyang Xu, Ziquan Zhuang
In this note, we discuss a number of open problems in K-stability theory.
Relative stability theory and properness of K-moduli spaces
Harold Blum, Yuchen Liu, Chenyang Xu +1
We define the relative stability threshold of a family of Fano varieties over a DVR and show that it is computed by a divisorial valuation. In the case when the special fiber is K-…
Boundedness of log Fano cone singularities and discreteness of local volumes
Chenyang Xu, Ziquan Zhuang
We prove that in any fixed dimension, K-semistable log Fano cone singularities whose volumes are bounded from below by a fixed positive number form a bounded set. As a consequence,…
Stability of klt singularities
Ziquan Zhuang
We survey some recent development in the stability theory of klt singularities. The main focus is on the solution of the stable degeneration conjecture.
Birational rigidity and alpha invariants of Fano varieties
Ivan Cheltsov, Arman Sarikyan, Ziquan Zhuang
We prove that for every , there is a birationally super-rigid Fano variety such that . Also we show that for every ,…