Optimal destabilization conjecture for K-unstable log Fano pairs
Optimal destabilization conjecture for K-unstable log Fano pairs
Let be a log Fano pair. For a divisor over , let denote its log discrepancy and let denote its expected vanishing order. The stability threshold is
Optimal destabilization conjecture. If is a K-unstable log Fano pair, then there exists a divisor over computing the infimum:
This asserts that the stability threshold of every K-unstable log Fano pair is attained by a divisorial valuation, providing an optimal destabilizing divisor and implying that the corresponding normalized Futaki infimum is a minimum. The supplied context does not state whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Harold Blum, Daniel Halpern-Leistner, Yuchen Liu and Chenyang Xu, “On properness of K-moduli spaces and optimal degenerations of Fano varieties”, arXiv:2011.01895 (2021).
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