Quasi-asymptotically conical Calabi-Yau manifolds
Abstract
We construct new examples of quasi-asymptotically conical (QAC) Calabi-Yau manifolds that are not quasi-asymptotically locally Euclidean (QALE). We do so by first providing a natural compactification of QAC-spaces by manifolds with fibred corners and by giving a definition of QAC-metrics in terms of an associated Lie algebra of smooth vector fields on this compactification. Thanks to this compactification and the Fredholm theory for elliptic operators on QAC-spaces developed by the second author and Mazzeo, we can in many instances obtain K\"ahler QAC-metrics having Ricci potential decaying sufficiently fast at infinity. This allows us to obtain QAC Calabi-Yau metrics in the K\"ahler classes of these metrics by solving a corresponding complex Monge-Amp\`ere equation.
Keywords
Cite
@article{arxiv.1611.04410,
title = {Quasi-asymptotically conical Calabi-Yau manifolds},
author = {Ronan J. Conlon and Anda Degeratu and Frédéric Rochon},
journal= {arXiv preprint arXiv:1611.04410},
year = {2019}
}
Comments
42 pages, 5 figures, final version