Desingularizations of CalabiYau 3folds with a conical singularity
Abstract
We study CalabiYau 3folds M_0 with a conical singularity x modelled on a CalabiYau cone V. We construct desingularizations of M_0, obtaining a 1parameter family of compact, nonsingular CalabiYau 3folds which has M_0 as the limit. The way we do is to choose an Asymptotically Conical CalabiYau 3fold 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 1parameter family of nearly CalabiYau 3folds M_t depending on a small real variable t. For sufficiently small t, we show that the nearly CalabiYau structures on M_t can be deformed to genuine CalabiYau 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 CalabiYau metrics on the crepant resolutions.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2004
 arXiv:
 arXiv:math/0410260
 Bibcode:
 2004math.....10260C
 Keywords:

 Differential Geometry;
 32Q25;
 53C29
 EPrint:
 29 pages