Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution
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 through 6 arising from Katz's theory of the middle convolution. A crucial role is played by the Mumford-Tate group (of type G2) of the family of 6-folds, and the theory of boundary components of Mumford-Tate domains.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2014
- DOI:
- 10.48550/arXiv.1407.4102
- arXiv:
- arXiv:1407.4102
- Bibcode:
- 2014arXiv1407.4102D
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Number Theory;
- 14D07;
- 14M17;
- 17B45;
- 20G99;
- 32M10;
- 32G20
- E-Print:
- 31 pages, 4 figures