Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising From Mirror Symmetry and Middle Convolution. (1st April 2016)

• Record Type: Journal Article
• Authors: da Silva, Genival; Kerr, Matt; Pearlstein, Gregory
• Is Part Of: Canadian journal of mathematics. Volume 68:Number 2(2016)
• Page Start: 280
• Page End: 308
• Publication Date: 2016-04-01
• Subjects: 14D07 -- 14M17 -- 17B45 -- 20G99 -- 32M10 -- 32G20; variation of Hodge structure -- limiting mixed Hodge structure -- Calabi–Yau variety -- middle convolution -- Mumford–Tate group; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2015-020-4
• Languages: English
• ISSNs: 0008-414X

Abstract

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.