Degenerations of Ricci-flat Calabi-Yau manifolds

Xiaochun Rong; Yuguang Zhang

doi:10.1142/S0219199712500575

Degenerations of Ricci-flat Calabi-Yau manifolds

Xiaochun Rong, Yuguang Zhang

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

This paper is a sequel to [Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differential Geom. 89 (2011) 233-270]. We further investigate the Gromov-Hausdorff convergence of Ricci-flat Kähler metrics under degenerations of Calabi-Yau manifolds. We extend Theorem 1.1 in [Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differential Geom. 89 (2011) 233-270] by removing the condition on existence of crepant resolutions for Calabi-Yau varieties.

Original language	English (US)
Article number	1250057
Journal	Communications in Contemporary Mathematics
Volume	15
Issue number	4
DOIs	https://doi.org/10.1142/S0219199712500575
State	Published - Aug 2013

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Calabi-Yau manifold
Gromov-Hausdorff convergence
degenerations

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10.1142/S0219199712500575

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title = "Degenerations of Ricci-flat Calabi-Yau manifolds",

abstract = "This paper is a sequel to [Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differential Geom. 89 (2011) 233-270]. We further investigate the Gromov-Hausdorff convergence of Ricci-flat K{\"a}hler metrics under degenerations of Calabi-Yau manifolds. We extend Theorem 1.1 in [Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differential Geom. 89 (2011) 233-270] by removing the condition on existence of crepant resolutions for Calabi-Yau varieties.",

keywords = "Calabi-Yau manifold, Gromov-Hausdorff convergence, degenerations",

author = "Xiaochun Rong and Yuguang Zhang",

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AU - Rong, Xiaochun

AU - Zhang, Yuguang

N1 - Funding Information: The first author was supported partially by NSF Grant DMS-1106517, and by research fund from Capital Normal University. The second author was supported by NSFC-11271015. The second author would like to thank Professor Jian Song for helpful discussions.

PY - 2013/8

Y1 - 2013/8

N2 - This paper is a sequel to [Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differential Geom. 89 (2011) 233-270]. We further investigate the Gromov-Hausdorff convergence of Ricci-flat Kähler metrics under degenerations of Calabi-Yau manifolds. We extend Theorem 1.1 in [Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differential Geom. 89 (2011) 233-270] by removing the condition on existence of crepant resolutions for Calabi-Yau varieties.

AB - This paper is a sequel to [Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differential Geom. 89 (2011) 233-270]. We further investigate the Gromov-Hausdorff convergence of Ricci-flat Kähler metrics under degenerations of Calabi-Yau manifolds. We extend Theorem 1.1 in [Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differential Geom. 89 (2011) 233-270] by removing the condition on existence of crepant resolutions for Calabi-Yau varieties.

KW - Calabi-Yau manifold

KW - Gromov-Hausdorff convergence

KW - degenerations

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Degenerations of Ricci-flat Calabi-Yau manifolds

Abstract

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