The 14th case VHS via K3 fibrations
Abstract
We present a study of certain singular one-parameter subfamilies of Calabi-Yau threefolds realized as anticanonical hypersurfaces or complete intersections in toric varieties. Our attention to these families is motivated by the Doran-Morgan classification of variations of Hodge structure which can underlie families of Calabi-Yau threefolds with over the thrice-punctured sphere. We explore their torically induced fibrations by -polarized K3 surfaces and use these fibrations to construct an explicit geometric transition between an anticanonical hypersurface and a nef complete intersection through a singular subfamily of hypersurfaces. Moreover, we show that another singular subfamily provides a geometric realization of the missing "14th case" variation of Hodge structure from the Doran-Morgan list.
Keywords
Cite
@article{arxiv.1312.6433,
title = {The 14th case VHS via K3 fibrations},
author = {Adrian Clingher and Charles F. Doran and Jacob Lewis and Andrey Y. Novoseltsev and Alan Thompson},
journal= {arXiv preprint arXiv:1312.6433},
year = {2016}
}