Séminaire de Géométrie Complexe

Critical Fubini-Study metrics over non-Archimedean fields

by Yanbo Fang

salle 207 bâtiment 1R2 (Institut de Mathématiques de Toulouse)

salle 207 bâtiment 1R2

Institut de Mathématiques de Toulouse

Critical Fubini-Study metrics on an ample line bundle are those minimizing (among its SL-orbits) the induced norm of the Chow form of the variety. Over complex numbers, such metrics are characterised by the constancy of its Bergman function (by S.-W. Zhang), and are known as balanced metrics in Kahler geometry (by Luo and Donaldson). We give an analogous result over a non-Archimedean field in terms of a polytope. (work based on arXiv:2212.02486)