About Kähler Quantization and the Calabi Problem

Julien Keller (1)

1 I2M - Institut de Mathématiques de Marseille

We explain how the Calabi problem on a smooth projective complex manifold can be discussed from the point of view of quantum formalism. We derive from this approach a natural flow on the space of Kähler potentials that has an interpretation in terms of moments maps. Finally, we discuss briefly how such techniques could be adapted to the study of the J-flow.

Mots clés: Calabi problem; Kahler metric; quantization; J-flow; projective manifold; moment map

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

Julien Keller. About Kähler Quantization and the Calabi Problem. Acta Physica Polonica B Proceedings Supplement, 2011, 4 (3), ⟨10.5506/APhysPolBSupp.4.325⟩. ⟨hal-01282482⟩