Résumé : Following the first part of the talk, we shall begin the second part by reviewing the notion of relative Chow stability, which is a version of GIT (Geometric Invariant Theory) stability for varieties with non-discrete automorphisms ; this is the stability condition that is implied by the quantisation of extremal Kähler metrics. There are in fact several versions of relative Chow stability, and each of them is studied in the literature (by e.g. Apostolov-Huang, Mabuchi, Sano-Tipler, Seyyedali). We shall see that each version is associated with a different characterisation of quantisation, which all agree when the automorphism group is discrete. We shall also see that their differences can be captured in terms of the quantity called the centre of mass, which is defined by the Kodaira embedding of the underlying Kähler manifold.
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