4 papers · 1 filter
The boundary of K-moduli of prime Fano threefolds of genus twelve
Anne-Sophie Kaloghiros, Yuchen Liu, Andrea Petracci +1
We study the K-moduli stack of prime Fano threefolds of genus twelve, known as . We prove that its boundary, which parametrizes singular members, is purely divisorial and c…
Optimal bounds for local volumes of threefold singularities
Yuchen Liu
We establish an optimal upper bound for local volumes of Gorenstein canonical non-hypersurface threefold singularities. Specifically, we show that a klt threefold singularity with…
Hassett--Keel Program in genus four
Kenneth Ascher, Kristin DeVleming, Yuchen Liu +1
The Hassett--Keel program seeks to give a modular interpretation to the steps of the log minimal model program of . The goal of this paper is to complete…
K-semistability of log Fano cone singularities
Yuchen Liu, Yueqiao Wu
We give a non-Archimedean characterization of K-semistability of log Fano cone singularities, and show that it agrees with the definition originally defined by Collins--Székelyhidi…