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arXiv · 1304.5216

Kähler currents and null loci

Tristan C. Collins·Valentino Tosatti
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Abstract

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.

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Tristan C. Collins, Valentino Tosatti. 2015-02-20. Kähler currents and null loci. https://doi.org/10.1007/s00222-015-0585-9

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