Type III contractions and quintic threefolds
Algebraic Geometry
2021-05-19 v3
Abstract
We study type III contractions of Calabi-Yau threefolds containing a ruled surface over a smooth curve. We discuss the conditions necessary for the image threefold to by smoothable. We describe the change in Hodge numbers caused by this contraction and smoothing deformation. A generalization of a fomula for calculating Hodge numbers of hypersurfaces in with ordinary double and triple points is presented. We use these results to construct new Calabi-Yau threefolds of Picard rank two arising from a family of quintic threefolds containing a cone.
Cite
@article{arxiv.2010.13866,
title = {Type III contractions and quintic threefolds},
author = {Kacper Grzelakowski},
journal= {arXiv preprint arXiv:2010.13866},
year = {2021}
}