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Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising From Mirror Symmetry and Middle Convolution

Published online by Cambridge University Press:  20 November 2018

Genival da Silva Jr. ,
Matt Kerr  and
Gregory Pearlstein
Genival da Silva Jr.
Affiliation:
Department of Mathematics, Campus Box 1146, Washington University in St. Louis, St. Louis, MO, USA e-mail: gffsjr@math.wustl.edu matkerr@math.wustl.edu
Matt Kerr
Affiliation:
Department of Mathematics, Campus Box 1146, Washington University in St. Louis, St. Louis, MO, USA e-mail: gffsjr@math.wustl.edu matkerr@math.wustl.edu
Gregory Pearlstein
Affiliation:
Mathematics Department, Mail stop 3368, Texas A&M University, College Station, TX 77843, USA e-mail: gpearl@math.tamu.edu
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Abstract

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We collect evidence in support of a conjecture of Griffiths, Green, and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degenerations over a number field. After briefly summarizing how a result of Iritani implies this conjecture for a collection of hypergeometric Calabi–Yau threefold examples studied by Doran and Morgan, the authors investigate a sequence of (non-hypergeometric) examples in dimensions $1\,\le \,d\,\le \,6$ arising from Katz's theory of the middle convolution. A crucial role is played by the Mumford-Tate group (which is ${{G}_{2}}$ ) of the family of 6-folds, and the theory of boundary components of Mumford–Tate domains.

Keywords

14D0714M1717B4520G9932M1032G20variation of Hodge structurelimiting mixed Hodge structureCalabi–Yau varietymiddle convolutionMumford–Tate group
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 2 , 01 April 2016 , pp. 280 - 308
Copyright
Copyright © Canadian Mathematical Society 2016

References

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