%0 Journal Article
%T The 14th case VHS via K3 fibrations
%A Adrian Clingher
%A Charles F. Doran
%A Jacob Lewis
%A Andrey Y. Novoseltsev
%A Alan Thompson
%J Mathematics
%D 2013
%I arXiv
%X 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 $h^{2,1} = 1$ over the thrice-punctured sphere. We explore their torically induced fibrations by $M$-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.
%U http://arxiv.org/abs/1312.6433v3