Fibering out Calabi-Yau motives

We prove the modularity of mixed periods associated with singular fibers of specific families of Calabi-Yau threefolds. This is done by “fibering out”, i.e. by expressing these periods as integrals of periods of families of K3 surfaces and by using modularity properties of the latter. Besides classical periods of holomorphic modular forms and meromorphic modular forms with vanishing residues, the computations lead to new interesting periods associated with meromorphic modular forms with non-vanishing residues as well as contours between CM points.