Geodesic
Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising From Mirror Symmetry and Middle Convolution
Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 280-308

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DOI

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.
DOI : 10.4153/CJM-2015-020-4
Mots-clés : 14D07, 14M17, 17B45, 20G99, 32M10, 32G20, variation of Hodge structure, limiting mixed Hodge structure, Calabi–Yau variety, middle convolution, Mumford–Tate group 
Jr., Genival da Silva; Kerr, Matt; Pearlstein, Gregory. Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising From Mirror Symmetry and Middle Convolution. Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 280-308. doi: 10.4153/CJM-2015-020-4
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     author = {Jr., Genival da Silva and Kerr, Matt and Pearlstein, Gregory},
     title = {Arithmetic of {Degenerating} {Principal} {Variations} of {Hodge} {Structure:} {Examples} {Arising} {From} {Mirror} {Symmetry} and {Middle} {Convolution}},
     journal = {Canadian journal of mathematics},
     pages = {280--308},
     year = {2016},
     volume = {68},
     number = {2},
     doi = {10.4153/CJM-2015-020-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-020-4/}
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