4 papers · 1 filter
On properness of K-moduli spaces and optimal degenerations of Fano varieties
Harold Blum, Daniel Halpern-Leistner, Yuchen Liu +1
We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable…
Reductivity of the automorphism group of K-polystable Fano varieties
Jarod Alper, Harold Blum, Daniel Halpern-Leistner +1
We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness a…
Uniqueness of K-polystable degenerations of Fano varieties
Harold Blum, Chenyang Xu
We prove that K-polystable degenerations of Q-Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable Q-Fano varieties is separated. Together with [Jia17,…
Openness of uniform K-stability in families of -Fano varieties
Harold Blum, Yuchen Liu
We show that uniform K-stability is a Zariski open condition in Q-Gorenstein families of Q-Fano varieties. To prove this result, we consider the behavior of the stability threshold…