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 develop a general approach to prove K-stability of Fano varieties. The new theory is
used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces …

We prove the existence of flips for $\mathbb Q $-factorial NQC generalized lc pairs, and the
cone and contraction theorems for NQC generalized lc pairs. This answers a question of C …

We prove that the ACC conjecture for minimal log discrepancies holds for threefolds in $[1-
\delta,+\infty) $, where $\delta> 0$ only depends on the coefficient set. We also study Reid's …

In this paper, we prove the rational coefficient case of the global ACC for foliated threefolds.
Specifically, we consider any lc foliated log Calabi-Yau triple $(X,\mathcal {F}, B) $ of …

We establish a Kollár-type gluing theory for NQC generalized log canonical pairs and use it
to prove semi-ampleness results of NQC generalized pairs. As consequences, we prove the …

arXiv:2012.06495v1 [math.AG] 11 Dec 2020 Existence and boundedness of n-complements
Page 1 arXiv:2012.06495v1 [math.AG] 11 Dec 2020 Existence and boundedness of n-complements …

We show Shokurov's complements conjecture holds for surfaces. More precisely, we show
the existence of (ϵ, n)-complements for (ϵ, R)-complementary surface pairs when the …

We study the relation between the coregularity, the index of log Calabi-Yau pairs, and the
complements of Fano varieties. We show that the index of a log Calabi-Yau pair $(X, B) $ of …

We prove that the first gap of $\mathbb R $-complementary thresholds of surfaces is $\frac
{1}{13} $. More precisely, the largest $\mathbb R $-complementary threshold for surfaces …