57 citations · 268 across the 15 of their papers we have counts for
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math.AG2018★ 22 cited
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★ 31 cited
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…
math.AG2018★ 30 cited
The normalized volume of a singularity is lower semicontinuous
Harold Blum, Yuchen Liu
We show that in any -Gorenstein flat family of klt singularities, normalized volumes are lower semicontinuous with respect to the Zariski topology. A quick consequence…