57 citations · 268 across the 15 of their papers we have counts for
16 papers
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…
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-…
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…
Moduli of boundary polarized Calabi-Yau pairs
Kenneth Ascher, Dori Bejleri, Harold Blum +4
We develop the moduli theory of boundary polarized CY pairs, which are slc Calabi-Yau pairs such that is ample. The motivation for studying this moduli problem is to co…
Convexity of multiplicities of filtrations on local rings
Harold Blum, Yuchen Liu, Lu Qi
We prove that the multiplicity of a filtration of a local ring satisfies various convexity properties. In particular, we show the multiplicity is convex along geodesics. As a conse…
The existence of the Kähler-Ricci soliton degeneration
Harold Blum, Yuchen Liu, Chenyang Xu +1
We prove an algebraic version of the Hamilton-Tian Conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a r…