activity
20162026
most citedUniqueness of the minimizer of the normalized volume function

14 citations · 24 across the 11 of their papers we have counts for

collaborators

29 papers

math.AG2026

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…

math.AG2026

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.

math.AG2025

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-…

math.AG2024★ 1 cited

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,…

math.AG2023

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.

math.AG2023★ 1 cited

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 ,…