  We prove that the non-Kahler locus of a nef and big class on a compact
complex manifold bimeromorphic to a Kahler manifold equals its null locus. In
particular this gives an analytic proof of a theorem of Nakamaye and
Ein-Lazarsfeld-Mustata-Nakamaye-Popa. As an application, we show that finite
time non-collapsing singularities of the Kahler-Ricci flow on compact Kahler
manifolds always form along analytic subvarieties, thus answering a question of
Feldman-Ilmanen-Knopf and Campana. We also extend the second author's results
about noncollapsing degenerations of Ricci-flat Kahler metrics on Calabi-Yau
manifolds to the nonalgebraic case.
