In this paper, we consider the CM line bundle on the K-moduli space, ie, the moduli space
parametrizing K-polystable Fano varieties. We prove it is ample on any proper subspace …

We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we
deduce this statement by establishing more general results concerning the S-completeness …

K-stability of Fano varieties: an algebro-geometric approach Page 1 EMS Surv. Math. Sci. 8 (2021),
265–354 DOI 10.4171/EMSS/51 © 2021 European Mathematical Society Published by EMS …

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 stability …

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 …

We prove an algebraic version of the Hamilton–Tian conjecture for all log Fano pairs. More
precisely, we show that any log Fano pair admits a canonical two-step degeneration to a …

We show that the K-moduli spaces of log Fano pairs (P 3, c S) where S is a quartic surface
interpolate between the GIT moduli space of quartic surfaces and the Baily–Borel …

We prove that for any $\mathbb {Q} $-Fano variety $ X $, the special $\mathbb {R} $-test
configuration that minimizes the $ H $-functional is unique and has a K-semistable $\mathbb …

We show that for a K–unstable Fano variety, any divisorial valuation computing its stability
threshold induces a nontrivial special test configuration preserving the stability threshold …

We construct proper good moduli spaces parametrizing K‐polystable QQ‐Gorenstein
smoothable log Fano pairs (X, c D) (X,cD), where XX is a Fano variety and DD is a rational …