Abstract: 

A consequence of Tian/Donaldson-Sun Partial C0 estimate is that non-collapsed Gromov-Hausdorff limits of polarized K\"ahler-Einstein manifolds are normal projective varieties. We extend their approach to the setting where only a lower bound for the Ricci curvature is assumed. More precisely, we show that non-collapsed Gromov-Hausdorff limits of polarized K\"ahler manifolds, with Ricci curvature bounded below, are normal projective varieties. In addition the metric singularities are precisely given by a countable union of analytic subvarieties.  This is a joint work with Gabor Szekelyhidi.