As on arXiv
Abstract
This is the first of two papers studying both the geometric structure of Fano fibrations and the application to Kähler-Ricci flows developing a singularity in finite time. Given a Fano fibration which is generated by Kawamata's theorem from a compact Kähler manifold endowed with an ample, rational line bundle and non-nef canonical line bundle , we construct a -form on the regular part of the base analytic variety which is related to the Weil-Petersson metric. It is also proven that the singular Kähler metric constructed by Zhang, Zhang, on the base analytic variety satisfies a twisted Kähler-Einstein equation involving this -form and, for a submersion, that the Chern classes of and the base manifold decompose in terms of this -form.
Comments: 21 pages
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Fano Fibrations and Twisted Kähler-Einstein Metrics II: The Kähler-Ricci Flow
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Same author Alexander Bednarek · Shared terms “twisted Kähler”, “Fano fibration”, “flow developing”
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On Miyaoka-Yau Inequalities and Weil-Petersson Metrics
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Same author Alexander Bednarek · Shared terms “Weil Petersson”, “line bundle”, “canonical line”
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Scalar Curvature, Volumes and the Bergman Kernel
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Shared terms “line bundle”, “canonical line”, “nef canonical”
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On almost nonpositive -Ricci curvature
Topics Analytic minimal model program, Kähler–Ricci flow, Kähler geometry · Shared terms “twisted Kähler”, “line bundle”, “canonical line”
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Global Ricci Curvature Behaviour for the Kähler-Ricci Flow with Finite Time Singularities
Topics Kähler–Ricci flow, Kähler geometry, Singularities · Same author Alexander Bednarek · Shared terms “analytic variety”, “finite time”, “rational”
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Gromov-Hausdorff limits of immortal Kähler-Ricci flows
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Shared terms “twisted Kähler”, “compact Kähler”
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Gromov-Hausdorff Convergence of Constant Scalar Curvature Kähler Metrics near the Canonical Class
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Shared terms “twisted Kähler”, “Zhang”, “compact Kähler”
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Continuity of solutions to complex Monge-Ampère equations on compact Kähler spaces
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Shared terms “compact Kähler”, “singular Kähler”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 5A.6Where This Track Leads
The Kähler–Ricci flow, and when to come back to it.
- 11B.4Blow-Ups, Blow-Downs and Splitting at Infinity
Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.
- 11B.6Rotationally Symmetric Flows and the Standard Solution
The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.