PreprintCC BY 4.0arXiv
Degenerations of exotic Calabi-Yau metrics through Atiyah's flop
Abstract
We construct new families of complete Calabi-Yau metrics with maximal volume growth on the small resolutions of the conifold 𝒵 = {z12 + z22 + z32 + z42 = 0} ⊂ ℂ4. These metrics have tangent cone ℂ × (ℂ2 / ℤ2) at infinity and are parametrised by their Kähler class. As the Kähler class degenerates, the metrics converge in the pointed Gromov-Hausdorff sense to a Calabi-Yau metric on 𝒵 with an isolated conical singularity modelled on the Stenzel metric at the ordinary double point and tangent cone at infinity ℂ × (ℂ2/ℤ2), thereby providing a new metric realisation of the Atiyah flop.
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BibTeX
@misc{langlais2026degenerations,
title = {{Degenerations of exotic Calabi-Yau metrics through Atiyah's flop}},
author = {Thibault Langlais and Viktor F. Majewski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08978},
eprint = {2609.08978},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08978},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Degenerations of exotic Calabi-Yau metrics through Atiyah's flop
AU - Thibault Langlais
AU - Viktor F. Majewski
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08978
UR - https://arxiv.org/abs/2609.08978
AB - We construct new families of complete Calabi-Yau metrics with maximal volume growth on the small resolutions of the conifold 𝒵 = {z_1^2 + z_2^2 + z_3^2 + z_4^2 = 0} ⊂ ℂ^4. These metrics have tangent cone ℂ × (ℂ^2 / ℤ_2) at infinity and are parametrised by their Kähler class. As the Kähler class degenerates, the metrics converge in the pointed Gromov-Hausdorff sense to a Calabi-Yau metric on 𝒵 with an isolated conical singularity modelled on the Stenzel metric at the ordinary double point and tangent cone at infinity ℂ × (ℂ^2/ℤ_2), thereby providing a new metric realisation of the Atiyah flop.
ER -