DEGENERATIONS OF RICCI-FLAT CALABI–YAU MANIFOLDS-Reference-Cited by-同舟云学术

DEGENERATIONS OF RICCI-FLAT CALABI–YAU MANIFOLDS

Published:2013-06-17 Issue:04 Volume:15 Page:1250057
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

RONG XIAOCHUN¹²,ZHANG YUGUANG¹

Affiliation:

1. Mathematics Department, Capital Normal University, Beijing 100048, P. R. China

2. Mathematics Department, Rutgers University, New Brunswick, NJ 08903, USA

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199712500575

Reference25 articles.

1. Ricci curvature bounds and Einstein metrics on compact manifolds

2. On the structure of spaces with Ricci curvature bounded below. I

3. Anti-Self-Duality of Curvature and Degeneration of Metrics with Special Holonomy

4. Singular Kähler-Einstein metrics

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