A decomposition formula for J-stability and its applications

2021/04/21 水 15:00 - 16:00
京都大学 数学教室

J-stability is an analog of K-stability and plays an important role in K-stability for general polarized varieties (not only for Kahler-Einstein metrics). Strikingly, G.Chen proved uniform J-stability and slope uniform J-stability are equivalent, analogous to Ross-Thomas slope theory and Mumford-Takemoto slope theory for vector bundles, 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 fact for surfaces and to construct a K-stable but not uniformly K-stable lc pair. Based on arXiv:2103.04603