  It is known that the scalar curvature arises as the moment map in Kahler
geometry. In pursuit of this analogy, we introduce the notion of a moment map
in generalized Kahler geometry which gives the definition of a generalized
scalar curvature on a generalized Kahler manifold. From the viewpoint of the
moment map, we obtain the generalized Ricci form which is a representative of
the first Chern class of the anticanonical line bundle. It turns out that
infinitesimal deformations of generalized Kahler structures with constant
generalized scalar curvature are finite dimensional on a compact manifold.
Explicit descriptions of the generalized Ricci form and the generalized scalar
curvature are given on a generalized Kahler manifold of type $(0,0)$. Poisson
structures constructed from a Kahler action of $T^m$ on a Kahler-Einstein
manifold give intriguing deformations of generalized Kahler-Einstein
structures. In particular, the anticanical divisor consists of three lines on
$C P^2$ in general position yields nontrivial examples of generalized
Kahler-Einsein structures
