3 papers
math.AG2019
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…
math.AG2018
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,…
math.AG2018
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…