6533b827fe1ef96bd1285b8e

RESEARCH PRODUCT

Hilbert modularity of some double octic Calabi--Yau threefolds

Sławomir CynkDuco Van StratenMatthias Schütt

subject

Modularity (networks)Pure mathematicsAlgebra and Number TheoryMathematics - Number Theory010102 general mathematicsModular formField (mathematics)010103 numerical & computational mathematics01 natural sciencesMathematics - Algebraic GeometryQuadratic equationMathematics::Algebraic GeometryFOS: MathematicsCalabi–Yau manifoldNumber Theory (math.NT)0101 mathematicsTwistHilbert modular formAlgebraic Geometry (math.AG)Mathematics

description

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.

yearjournalcountryeditionlanguage
2018-10-10
http://arxiv.org/abs/1810.04495