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

作者：da Silva Genival Jr^*; Kerr Matt^*; Pearlstein Gregory^*

来源：Canadian Journal of Mathematics, 2016, 68(2): 280-308.

DOI：10.4153/CJM-2015-020-4

• variation of Hodge structure
• limiting mixed Hodge structure
• Calabi-Yau variety
• middle convolution
• Mumford-Tate group

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 <= d <= 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.

• 出版日期2016-4