Details
| Original language | English |
|---|---|
| Pages (from-to) | 313-332 |
| Number of pages | 20 |
| Journal | Journal of number theory |
| Volume | 210 |
| Publication status | Published - 1 May 2020 |
Abstract
Keywords
- Calabi-Yau threefold, Double octic, Faltings–Serre–Livné method, Hilbert modularity
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of number theory, Vol. 210, 01.05.2020, p. 313-332.
Research output: Contribution to journal › Article › Research › peer review
}
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 -