Title: Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces,
Abstract: 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.