Desingularizations of Calabi-Yau 3-folds with a conical singularity

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dc.creatorChan, Yat-Ming
dc.date2004-10-11
dc.date.accessioned2026-07-07T05:13:09Z
dc.date.available2026-07-07T05:13:09Z
dc.descriptionWe study Calabi-Yau 3-folds M_0 with a conical singularity x modelled on a Calabi-Yau cone V. We construct desingularizations of M_0, obtaining a 1-parameter family of compact, nonsingular Calabi-Yau 3-folds which has M_0 as the limit. The way we do is to choose an Asymptotically Conical Calabi-Yau 3-fold Y modelled on the same cone V, and then glue into M_0 at x after applying a homothety to Y. We then get a 1-parameter family of nearly Calabi-Yau 3-folds M_t depending on a small real variable t. For sufficiently small t, we show that the nearly Calabi-Yau structures on M_t can be deformed to genuine Calabi-Yau structures, and therefore obtaining the desingularizations of M_0. Our result can be applied to resolving orbifold singularities and hence provides a quantitative description of the Calabi-Yau metrics on the crepant resolutions.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0410260
dc.identifierhttp://arxiv.org/abs/math/0410260
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72840
dc.subjectDifferential Geometry
dc.subject32Q25, 53C29
dc.titleDesingularizations of Calabi-Yau 3-folds with a conical singularity
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