A moment map interpretation of the Ricci form, Kähler--Einstein structures, and Teichmüller spaces

2020/04/18 by Garcia-Prada, Oscar, Salamon, Dietmar
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2004.08659

Abstract

This paper surveys the role of moment maps in Kähler geometry. The first section discusses the Ricci form as a moment map and then moves on to moment map interpretations of the Kähler--Einstein condition and the scalar curvature (Quillen--Fujiki--Donaldson). The second section examines the ramifications of these results for various Teichmüller spaces and their Weil--Petersson symplectic forms and explains how these arise naturally from the construction of symplectic quotients. The third section discusses a symplectic form introduced by Donaldson on the space of Fano complex structures.

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