A moment map interpretation of the Ricci form, K\"ahler--Einstein structures, and Teichm\"uller spaces

This paper surveys the role of moment maps in K"ahler geometry. The first section discusses the Ricci form as a moment map and then moves on to moment map interpretations of the K"ahler–Einstein condition and the scalar curvature (Quillen–Fujiki–Donaldson). The second section examines the ramifications of these results for various Teichm"uller 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.