Remarks on the collapsing of torus fibered Calabi-Yau manifolds

Abstract

One of the main results of the paper arXiv:1108.0967 by Gross-Tosatti-Zhang establishes estimates on the collapsing of Ricci-flat Kahler metrics on holomorphic torus fibrations. We remove a projectivity assumption from these estimates and simplify some of the underlying analysis.

6 pages; final version to appear in Bull. Lond. Math. Soc

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• Nakamaye's theorem on complex manifolds
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• Local curvature estimates of long-time solutions to the Kähler-Ricci flow
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• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• The continuity method on minimal elliptic Kähler surfaces
• Infinite-time singularity type of the Kähler-Ricci flow
• Smooth asymptotics for collapsing Calabi-Yau metrics
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• Twisted Kähler-Einstein Metrics and Collapsing
• Leafwise flat forms on Inoue-Bombieri surfaces
• Special Kähler geometry and holomorphic Lagrangian fibrations
• Degeneration of Ricci-flat Calabi-Yau manifolds and its applications
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• Collapsing immortal Kähler-Ricci flows
• A note on conical Kähler-Ricci flow on minimal elliptic Kähler surfaces
• On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows
• Integral inequalities for holomorphic maps and applications