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Title: The 14th case VHS via K3 fibrations
Authors: Clingher, Adrian
Doran, Charles F.
Lewis, Jacob
Novoseltsev, A.Y.
Thompson, Alan
Issue Date: 2016
Publisher: © Cambridge University Press
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.
Series/Report no.: London Mathematical Society Lecture Note Series;427
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.
Description: 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
Sponsor: 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.
Version: Accepted for publication
DOI: 10.1017/CBO9781316387887.008
URI: https://dspace.lboro.ac.uk/2134/35218
Publisher Link: https://doi.org/10.1017/CBO9781316387887.008
ISBN: 9781316387887
ISSN: 0076-0552
Appears in Collections:Published Articles (Maths)

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