Optimal destabilization of K–unstable Fano varieties via stability thresholds
Optimal destabilization of K–unstable Fano varieties via stability thresholds
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 threshold.When such a divisorial valuation exists, we show that the Fano variety degenerates to a uniquely determined twisted K-polystable Fano variety.We also show that the stability …