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Monge-Ampère degenerations and conifold contractions in Fujiki class 𝒞
Abstract
Given a ℚ-Gorenstein normal projective Calabi-Yau variety Y with ordinary double points as singularities and a small crepant resolution π: X→ Y with X in the Fujiki class 𝒞, we establish uniform estimates away from the exceptional locus where the given metrics may degenerate. When Y is a threefold, we prove that these metrics also converge in a Gromov-Hausdorff sense to the metric completion of Y on the regular locus. In particular, our results extend the work of Song on a conjecture of Candelas and de la Ossa.
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BibTeX
@misc{guyett2026mongeampère,
title = {{Monge-Ampère degenerations and conifold contractions in Fujiki class $\mathcalC$}},
author = {Riley Guyett and Ryan Mc Gowan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00942},
eprint = {2610.00942},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00942},
}
RIS
TY - UNPB
TI - Monge-Ampère degenerations and conifold contractions in Fujiki class 𝒞
AU - Riley Guyett
AU - Ryan Mc Gowan
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00942
UR - https://arxiv.org/abs/2610.00942
AB - Given a ℚ-Gorenstein normal projective Calabi-Yau variety Y with ordinary double points as singularities and a small crepant resolution π: X→ Y with X in the Fujiki class 𝒞, we establish uniform estimates away from the exceptional locus where the given metrics may degenerate. When Y is a threefold, we prove that these metrics also converge in a Gromov-Hausdorff sense to the metric completion of Y on the regular locus. In particular, our results extend the work of Song on a conjecture of Candelas and de la Ossa.
ER -