Continuity of Extremal Transitions and Flops for Calabi-Yau Manifolds
Abstract
In this paper, we study the behavior of Ricci-flat Kähler metrics on Calabi-Yau manifolds under algebraic geometric surgeries: extremal transitions or flops. We prove a version of Candelas and de la Ossa's conjecture: Ricci-flat Calabi-Yau manifolds related by extremal transitions and flops can be connected by a path consisting of continuous families of Ricci-flat Calabi-Yau manifolds and a compact metric space in the Gromov-Hausdorff topology. In an essential step of the proof of our main result, the convergence of Ricci-flat Kähler metrics on Calabi-Yau manifolds along a smoothing is established, which can be of independent interests.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2010
- DOI:
- 10.48550/arXiv.1012.2940
- arXiv:
- arXiv:1012.2940
- Bibcode:
- 2010arXiv1012.2940R
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Algebraic Geometry;
- Mathematics - Metric Geometry
- E-Print:
- An appendix is written by Mark Gross