Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising From Mirror Symmetry and Middle Convolution. (1st April 2016) - da Silva, Genival; Kerr, Matt; Pearlstein, Gregory
Abstract: 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.