57 citations · 268 across the 15 of their papers we have counts for
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Optimal destabilization of K-unstable Fano varieties via stability thresholds
Harold Blum, Yuchen Liu, Chuyu Zhou
We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a non-trivial special test configuration preserving the stability thr…
Openness of K-semistability for Fano varieties
Harold Blum, Yuchen Liu, Chenyang Xu
In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also pro…
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…