Kähler currents and null loci
By Tristan C. Collins, Valentino Tosatti. 2013
111 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ce298f41495b8c66c9c1f87251855b314939a246
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In Applied Mathematics
- Xiaokui Yang
- Valentino Tosatti
- B. Weinkove
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Fang Zheng
- Dat T. To
- M. Gill
In Geometry and Topology
- Xiaokui Yang
- Valentino Tosatti
- B. Weinkove
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Fang Zheng
- Dat T. To
- M. Gill
Citations in the corpus
- The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits (2014, background): “By comparison, in the case when the volume of the Ricci-flat metrics is non-collapsing, we have a very thorough understanding of their limiting behavior, thanks to the results in [8, 31, 32, 33, 37, 53], and all the analogous questions have affirmative answers.”
- KAWA lecture notes on the Kähler-Ricci flow (2015, background): “Next, in Section 4 we discuss finite time singularities, both volume noncollapsed and volume collapsed, in particular giving a characterization of the singularity formation set, due to Collins and the author [10].”