Smoothing nodal Calabi-Yau n-folds
Algebraic Geometry
2019-12-05 v3 Differential Geometry
Abstract
Let X be an n-dimensional Calabi-Yau with ordinary double points, where n is odd. Friedman showed that for n=3 the existence of a smoothing of X implies a specific type of relation between homology classes on a resolution of X. (The converse is also true, due to work of Friedman, Kawamata and Tian.) We sketch a more topological proof of this result, and then extend it to higher dimensions. For n>3 the "Yukawa product" on the middle dimensional (co)homology plays an unexpected role. We also discuss a converse, proving it for nodal Calabi-Yau hypersurfaces in projective space.
Keywords
Cite
@article{arxiv.0810.0141,
title = {Smoothing nodal Calabi-Yau n-folds},
author = {S. Rollenske and R. P. Thomas},
journal= {arXiv preprint arXiv:0810.0141},
year = {2019}
}
Comments
Included missing torsion in Lemma 2.5. Results unchanged. 20 pages