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The 14th case VHS via K3 fibrations

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posted on 2018-10-08, 11:02 authored by Adrian Clingher, Charles F. Doran, Jacob Lewis, A.Y. Novoseltsev, Alan ThompsonAlan Thompson
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.

Funding

A. Clingher was supported by Simons Foundation grant no. 208258 and by a Bitdefender Invited Professor scholarship from IMAR. C. F. Doran and A. Y. Novoseltsev were supported by the Natural Sciences and Engineering Resource Council of Canada (NSERC), the Pacific Institute for the Mathematical Sciences, and the McCalla Professorship at the University of Alberta. J. Lewis was supported in part by NSF grant OISE-0965183. A. Thompson was supported in part by NSERC and in part by a Fields Institute Ontario Postdoctoral Fellowship with funding provided by NSERC and the Ontario Ministry of Training, Colleges and Universities.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

London Mathematical Society Lecture Note Series

Volume

427

Pages

165 - 227

Citation

CLINGHER, A. ... et al., 2016. The 14th case VHS via K3 fibrations. IN: Kerr, M. and Pearlstein, G. (eds.) Recent Advances in Hodge Theory: Period Domains, Algebraic Cycles, and Arithmetic. Cambridge: Cambridge University Press, pp. 165-227.

Publisher

© Cambridge University Press

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016-02-01

Notes

This material has been published in Recent Advances in Hodge Theory: Period Domains, Algebraic Cycles, and Arithmetic edited by Kerr, M. and Pearlstein, G. This version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press. The final published version can be found here: https://doi.org/10.1017/CBO9781316387887.008

ISBN

9781316387887

ISSN

0076-0552

Book series

London Mathematical Society Lecture Note Series;427

Language

  • en

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