TY - JOUR

T1 - Hilbert modularity of some double octic Calabi–Yau threefolds

AU - Cynk, Sławomir

AU - Schütt, Matthias

AU - van Straten, Duco

N1 - Funding information: The first named author was partially supported by the National Science Center grant no. 2014/13/B/ST1/00133. This research was supported in part by PLGrid Infrastructure. Partial funding by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund is gratefully acknowledged.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - We exhibit three double octic Calabi--Yau threefolds over the certain quadratic fields and prove their modularity. The non-rigid threefold has two conjugate Hilbert modular forms 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.

AB - We exhibit three double octic Calabi--Yau threefolds over the certain quadratic fields and prove their modularity. The non-rigid threefold has two conjugate Hilbert modular forms 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.

KW - Calabi-Yau threefold

KW - Double octic

KW - Faltings–Serre–Livné method

KW - Hilbert modularity

UR - http://www.scopus.com/inward/record.url?scp=85074531800&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2019.09.015

DO - 10.1016/j.jnt.2019.09.015

M3 - Article

AN - SCOPUS:85074531800

VL - 210

SP - 313

EP - 332

JO - Journal of number theory

JF - Journal of number theory

SN - 0022-314X

ER -