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On the degeneration of asymptotically conical Calabi-Yau metrics

Authors :
Collins, Tristan C.
Guo, Bin
Tong, Freid
Publication Year :
2020

Abstract

We study the degenerations of asymptotically conical Ricci-flat K\"ahler metrics as the K\"ahler class degenerates to a semi-positive class. We show that under appropriate assumptions, the Ricci-flat K\"ahler metrics converge to a incomplete smooth Ricci-flat K\"ahler 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.<br />Comment: 40 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2006.15752
Document Type :
Working Paper