Phase transition of Kähler-Einstein metrics via moment maps
type: Item
instance of: scholarly article
title: Phase transition of Kähler-Einstein metrics via moment maps
zbMATH Open document ID: 1431.53079
author: Xianqiang Yang
published in: Communications in Mathematics and Statistics
publication date: 2019-01-02T00:00:00Z
review text: 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.
reviewed by: Manuel de León
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53D20
zbMATH DE Number: 6997214
zbMATH Keywords: moment map
zbMATH Keywords: phase transition
zbMATH Keywords: Kähler-Einstein space
MaRDI profile type: Publication
full work available at URL: s40304-018-0153-x
OpenAlex ID: W2889110186
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DOI: 10.1007/S40304-018-0153-X
description: scientific article; zbMATH DE number 6997214