Kahler currents and null loci

• 成果类型: Article
• 署名作者: Collins, Tristan C.; Tosatti, Valentino
• 署名单位: Harvard University; Northwestern University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0585-9
• 发表日期: 2015
• 页码: 1167-1198
• 关键词: finite-time singularity; einstein metrics; projective-manifolds; ricci flow; base loci; asymptotics; VARIETIES; extension; CURVATURE; STABILITY

摘要

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-Musta-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.