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math.AG2026
Valuative independence for Calabi--Yau varieties
Harold Blum, Yuchen Liu
We construct valuatively independent bases for the space of sections of an ample line bundle on a log Calabi--Yau pair over a discretely valued field and the space of regular funct…
math.AG2025
Relative stability theory and properness of K-moduli spaces
Harold Blum, Yuchen Liu, Chenyang Xu +1
We define the relative stability threshold of a family of Fano varieties over a DVR and show that it is computed by a divisorial valuation. In the case when the special fiber is K-…
math.AG2024
Good moduli spaces for boundary polarized Calabi-Yau surface pairs
Harold Blum, Yuchen Liu
We construct projective asymptotically good moduli spaces parametrizing boundary polarized CY surface pairs, which are projective slc Calabi-Yau pairs such that is ampl…