  We show that non-collapsed Gromov-Hausdorff limits of polarized Kahler
manifolds, with Ricci curvature bounded below, are normal projective varieties,
and the metric singularities of the limit space are precisely given by a
countable union of analytic subvarieties. This extends a fundamental result of
Donaldson-Sun, in which 2-sided Ricci curvature bounds were assumed. As a basic
ingredient we show that, under lower Ricci curvature bounds, almost Euclidean
balls in Kahler manifolds admit good holomorphic coordinates. Further
applications are integral bounds for the scalar curvature on balls, and a
rigidity theorem for Kahler manifolds with almost Euclidean volume growth.
