On the degeneration of asymptotically conical Calabi–Yau metrics
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Author(s)
Collins, Tristan C.
Guo, Bin
Tong, Freid
Date Issued
June 28, 2021
Publisher
Springer Berlin Heidelberg
Citation
Collins, Tristan C., Guo, Bin and Tong, Freid. 2021. "On the degeneration of asymptotically conical Calabi–Yau metrics."
Version
Author's final manuscript
Abstract
Abstract
We study the degenerations of asymptotically conical Ricci-flat Kähler metrics as the Kähler class degenerates to a semi-positive class. We show that under appropriate assumptions, the Ricci-flat Kähler metrics converge to a incomplete smooth Ricci-flat Kähler metric away from a compact subvariety. As a consequence, we construct singular Calabi–Yau metrics with asymptotically conical behaviour at infinity on certain quasi-projective varieties and we show that the metric geometry of these singular metrics are homeomorphic to the topology of the singular variety. Finally, we will apply our results to study several classes of examples of geometric transitions between Calabi–Yau manifolds.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00208-021-02229-z
