In this paper, we study the ascending chain condition (ACC) conjecture for minimal log
discrepancies (mlds), proposed by the third author. We show the ACC conjecture holds for …

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 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 prove that rationally connected Calabi–Yau 3-folds with Kawamata log terminal (klt)
singularities form a birationally bounded family, or more generally, rationally connected 3 …

Recent study in K-stability suggests that klt singularities whose local volumes are bounded
away from zero should be bounded up to special degeneration. We show that this is true in …

A conic bundle is a contraction between normal varieties of relative dimension such that is
relatively ample. We prove a conjecture of Shokurov that predicts that if is a conic bundle …

An optimal gap of minimal log discrepancies of threefold non-canonical singularities -
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We systematically introduce and study a new type of singularity, namely, exceptionally
noncanonical (enc) singularities. This class of singularities plays an important role in the …

We present an extension of several results on pairs and varieties to foliated surface pairs.
We prove the boundedness of local complements, the local index theorem, and the uniform …