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 study the relationship between Iitaka fibrations and the conjecture on the existence of
complements, assuming the good minimal model conjecture. In one direction, we show that …

We give an explicit characterization on the singularities of exceptional pairs in any
dimension. In particular, we show that any exceptional Fano surface is-lc. As corollaries, we …

Let $\Gamma $ be a finite set, and $ X\ni x $ a fixed kawamata log terminal germ. For any lc
germ $(X\ni x, B:=\sum _ {i} b_iB_i) $, such that $ b_i\in\Gamma $, Nakamura's conjecture …

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 …

In this paper, we study the theory of complements, introduced by Shokurov, for Calabi–Yau
type varieties with the coefficient set [0, 1]. We show that there exists a finite set of positive …

arXiv:2202.11346v3 [math.AG] 1 Jun 2023 Page 1 arXiv:2202.11346v3 [math.AG] 1 Jun 2023
ACC FOR FOLIATED LOG CANONICAL THRESHOLDS YEN-AN CHEN Abstract. It is known …

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 …

arXiv:2207.04610v1 [math.AG] 11 Jul 2022 Page 1 arXiv:2207.04610v1 [math.AG] 11 Jul 2022
SECOND LARGEST ACCUMULATION POINT OF MINIMAL LOG DISCREPANCIES OF …

In this paper, we continue to develop the theories on functional pairs and uniform rational
polytopes. We show that there is a uniform perturbation for Iitaka dimensions of pseudo …