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math.AG2025
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…
math.AG2025
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…