Hilbert modularity of some double octic Calabi-Yau threefolds

JOURNAL OF NUMBER THEORY

卷:210

Article

Cynk, Slawomir¹  Schuett, Matthias^2,3  van Straten, Duco⁴ 

[1] Jagiellonian Univ, Inst Math, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

[2] Leibniz Univ Hannover, Inst Algebra Geometr, Welfengarten 1, D-30167 Hannover, Germany

[3] Leibniz Univ Hannover, Riemann Ctr Geometry & Phys, Appelstr 2, D-30167 Hannover, Germany

[4] Johannes Gutenberg Univ Mainz, Inst Math, Phys Math & Informat FB 08, Staudingerweg 9, D-55128 Mainz, Germany

关键词: Calabi-Yau threefold;    Hilbert modularity;    Double octic;    Faltings-Serre-Livne method;   

DOI  :  10.1016/j.jnt.2019.09.015

来源: Elsevier

【 摘 要 】

We exhibit three double octic Calabi-Yau threefolds, a non-rigid threefold defined over Q and two rigid threefolds over the quadratic fields Q [root 5], Q [root-3], and prove their modularity. The non-rigid threefold has two conjugate Hilbert modular forms for the field Q [root 2] of weight [4, 2] and [2,4] attached while the two rigid threefolds correspond to a Hilbert modular form of weight [4, 4] and to the twist of the restriction of a classical modular form of weight 4. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free