2018/10/10 by Slawomir Cynk, Matthias Schütt, Cynk, Slawomir +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.1810.04495
12 pages
arxiv created 2018/10/10 · arxiv updated 2018/10/11
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.