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arXiv · 1701.03279

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

Charles F. Doran·Andrew Harder·Andrey Y. Novoseltsev·Alan Thompson
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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.

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Charles F. Doran, Andrew Harder, Andrey Y. Novoseltsev, Alan Thompson. 2017-01-12. Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces. https://doi.org/10.1007/s00209-019-02279-9

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