Phase transition of Kähler-Einstein metrics via moment maps (Q1757191)

This paper is devoted to study the phase transition phenomena of Kähler metrics from the symplectic point of view. Let us explain this fact. The limit metric of Kähler-Einstein metrics may degenerate along a subvariety, and to understand such degenerations it is useful to study the behavior of the metric near the subvariety. The authors use the \(U(n)\) symmetry to reduce the problem and they introduce a phenomenon called the phase transition of Kähler metrics (the terminology is borrowed from physics). Indeed, one can use symplectic techniques considering the moment map of natural torus actions, so that the polytope theory gives new and surprising insights into the subject. This paper is a brilliant combination of the phase transition method and the convexity properties of the corresponding moment maps.