Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces

Understand

We study threefolds fibred by K3 surfaces admitting a lattice polarization by a certain class of rank 19 lattices.

• We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the appropriate K3 moduli space, which we call the generalized functional invariant.
• Then we show that if the threefold total space is a smooth Calabi-Yau, there are only finitely many possibilities for the polarizing lattice and the form of the generalized functional invariant.
• Finally, we construct explicit examples of Calabi-Yau threefolds realizing each case and compute their Hodge numbers.