Degenerations of Ricci-flat Calabi-Yau manifolds

Yuguang Zhang; Xiaochun Rong

doi:10.1142/S0219199712500575

Degenerations of Ricci-flat Calabi-Yau manifolds

Yuguang Zhang
, Xiaochun Rong

Capital Normal University

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

8 Citations (Scopus)

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
Article number	1250057
Journal	Communications in Contemporary Mathematics
Volume	15
Issue number	4
DOIs	https://doi.org/10.1142/S0219199712500575
Publication status	Published - Aug 2013
Externally published	Yes

Keywords

Calabi-Yau manifold
degenerations
Gromov-Hausdorff convergence

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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.",

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AU - Rong, Xiaochun

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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 - degenerations

KW - Gromov-Hausdorff convergence

UR - https://www.scopus.com/pages/publications/84874353874

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DO - 10.1142/S0219199712500575

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JO - Communications in Contemporary Mathematics

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ER -

Degenerations of Ricci-flat Calabi-Yau manifolds

Abstract

Keywords

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