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) …

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 …

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 existence of twisted Kähler–Einstein metrics in big cohomology classes, using a
divisorial stability condition. In particular, when− KX -K_X is big, we obtain a uniform Yau …