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K\"ahler currents and null loci
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.Comment: 29 pages, 1 figure; small improvements, final version to appear in
Invent. Mat
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