Nonuniqueness of Calabi-Yau metrics with maximal volume growth
Abstract
We construct a family of inequivalent Calabi-Yau metrics on $\mathbf{C}^3$ asymptotic to $\mathbf{C} \times A_2$ at infinity, in the sense that any two of these metrics cannot be related by a scaling and a biholomorphism. This provides the first example of families of Calabi-Yau metrics asymptotic to a fixed tangent cone at infinity, while keeping the underlying complex structure fixed. We propose a refinement of a conjecture of Székelyhidi addressing the classification of such metrics.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.08210
- arXiv:
- arXiv:2206.08210
- Bibcode:
- 2022arXiv220608210C
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- 24 pages