Openness of K-semistability for Fano varieties
Harold Blum, Yuchen Liu, Chenyang Xu
Abstract
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 prove that any special test configuration arises from a log canonical place of a bounded complement and establish properties of any minimizer of the stability threshold.
Topics & Concepts
Fano planeMathematicsOpenness to experienceComplement (music)Stability (learning theory)Bounded functionPure mathematicsFunction (biology)CombinatoricsMathematical analysisComputer scienceChemistryPsychologyComplementationGeneBiologyMachine learningPhenotypeSocial psychologyEvolutionary biologyBiochemistryGeometry and complex manifoldsGeometric Analysis and Curvature FlowsAlgebraic Geometry and Number Theory