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

被引：5

作者：

da Silva, Genival, Jr. ^{[1
]}

Kerr, Matt ^{[1
]}

Pearlstein, Gregory ^{[2
]}

机构：

[1] Washington Univ, Dept Math, Campus Box 1146, St Louis, MO 63130 USA

[2] Texas A&M Univ, Dept Math, Mail Stop 3368, College Stn, TX 77843 USA

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2016年 / 68卷 / 02期

基金：

美国国家科学基金会;

关键词：

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

D O I：

10.4153/CJM-2015-020-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：280 / 308

页数：29