We prove that on any log Fano pair of dimension n whose stability threshold is less than
n+1n, any valuation computing the stability threshold has a finitely generated associated …

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 prove …

We give an algebraic proof of the equivalence of equivariant K-semistability (resp.
equivariant K-polystability) with geometric K-semistability (resp. geometric K-polystability) …

Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds
are a fundamental subclass that can be thought of as higher-dimensional generalizations of …

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 …

We develop the moduli theory of boundary polarized CY pairs, which are slc Calabi-Yau
pairs $(X, D) $ such that $ D $ is ample. The motivation for studying this moduli problem is to …

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 …

Let X be any Q Q-Fano variety and Aut (X) _0 Aut (X) 0 be the identity component of the
automorphism group of X. Let GG be a connected reductive subgroup of Aut (X) _0 Aut (X) 0 …

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 …