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arXiv · 1312.6433

The 14th case VHS via K3 fibrations

Adrian Clingher·Charles F. Doran·Jacob Lewis·Andrey Y. Novoseltsev·Alan Thompson
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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 $h^{2,1} = 1$ 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.

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Adrian Clingher, Charles F. Doran, Jacob Lewis, Andrey Y. Novoseltsev, Alan Thompson. 2013-12-22. The 14th case VHS via K3 fibrations. https://doi.org/10.1017/cbo9781316387887.008

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