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• W3098299265 abstract "We study the collapsing behavior of Ricci-flat Kähler metrics on a projective Calabi–Yau manifold which admits an abelian fibration, when the volume of the fibers approaches zero. We show that away from the critical locus of the fibration the metrics collapse with locally bounded curvature, and along the fibers the rescaled metrics become flat in the limit. The limit metric on the base minus the critical locus is locally isometric to an open dense subset of any Gromov–Hausdorff limit space of the Ricci-flat metrics. We then apply these results to study metric degenerations of families of polarized hyperkähler manifolds in the large complex structure limit. In this setting, we prove an analogue of a result of Gross and Wilson for K3 surfaces, which is motivated by the Strominger–Yau–Zaslow picture of mirror symmetry." @default.
• W3098299265 created "2020-11-23" @default.
• W3098299265 creator A5036588454 @default.
• W3098299265 creator A5043707556 @default.
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• W3098299265 date "2013-02-15" @default.
• W3098299265 modified "2023-10-17" @default.
• W3098299265 title "Collapsing of abelian fibered Calabi–Yau manifolds" @default.
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• W3098299265 doi "https://doi.org/10.1215/00127094-2019703" @default.
• W3098299265 hasPublicationYear "2013" @default.
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