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 …

This book gives a comprehensive treatment of the singularities that appear in the minimal
model program and in the moduli problem for varieties. The study of these singularities and …

We prove a version of Jonsson-Mustaţǎ's Conjecture, which says for any graded sequence
of ideals, there exists a quasi-monomial valuation computing its log canonical threshold. As …

We study the topology of a space $\Delta _ {g} $ parametrizing stable tropical curves of
genus $ g $ with volume $1 $, showing that its reduced rational homology is canonically …

We prove two new results on the $ K $-polystability of $\mathbb {Q} $-Fano varieties based
on purely algebro-geometric arguments. The first one says that any $ K $-semistable log …

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 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 …

We study the asymptotic behavior of volume forms on a degenerating family of compact
complex manifolds. Under rather general conditions, we prove that the volume forms …

Let be a pair, and let be a contraction with nef over S. A conjecture, known as the Shokurov–
Kollár connectedness principle, predicts that has at most two connected components, where …

Abstract The Chow–Mumford (CM) line bundle is a functorial line bundle on the base of any
family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space …