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Abstract:
J-stability plays an important role in K-stability and deeply related to the existence of a stationary solution of J-flow. Strikingly, G. Chen, Datar Pingali and J. Song proved Lejmi-Szekelyhidi conjecture, uniform J-stability and J-positivity are equivalent, by differential geometric arguments recently. However, this fact has not been proved in algebro-geometric way before. In this talk, I would like to explain a decomposition formula of non-Archimedean J-functional, the (n+1)-dimensional intersection number into n-dimensional intersection numbers and its applications to prove the conjecture for singular algebraic surfaces and to show that there exists a J-stable but not uniformly J-stable variety.
Based on arXiv:2103.04603