Nonuniqueness of CalabiYau metrics with maximal volume growth
Abstract
We construct a family of inequivalent CalabiYau 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 CalabiYau 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:

arXiv eprints
 Pub Date:
 June 2022
 DOI:
 10.48550/arXiv.2206.08210
 arXiv:
 arXiv:2206.08210
 Bibcode:
 2022arXiv220608210C
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 24 pages