Kähler currents and null loci
Kähler currents and null loci
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DOI：
10.1007/s00222-015-0585-9
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发表时间：
2013-04
影响因子：
3.1
通讯作者：
Tristan C. Collins;Valentino Tosatti
中科院分区：
文献类型：
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作者：
Tristan C. Collins;Valentino Tosatti
本文证明了双纯于Kähler流形的紧致复流形上的nef大类的非Kähler轨迹等于它的零轨迹。特别是这给出了一个定理的分析证明Nakamaye和艾因-Lazarsfeld-Mustafel-Nakamaye-Popa。作为应用，我们证明了紧致Kähler流形上Kähler-Ricci流的有限时间非坍缩奇点总是沿沿着解析子簇形成，从而回答了Feldman-Ilmanen-Knopf和Campana的一个问题.我们还将第二作者关于Calabi-Yau流形上Ricci平坦Kähler度量的非塌缩退化的结果推广到非代数情形。
We prove that the non-Kähler locus of a nef and big class on a compact complex manifold bimeromorphic to a Kähler manifold equals its null locus. In particular this gives an analytic proof of a theorem of Nakamaye and Ein–Lazarsfeld–Mustaţă–Nakamaye–Popa. As an application, we show that finite time non-collapsing singularities of the Kähler–Ricci flow on compact Kähler 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 Kähler metrics on Calabi–Yau manifolds to the nonalgebraic case.