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

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posted on 12.03.2019 by Charles F. Doran, Andrew Harder, A.Y. Novoseltsev, Alan Thompson
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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School

  • Science

Department

  • Mathematical Sciences

Published in

Mathematische Zeitschrift

Volume

294

Pages

783–815

Citation

DORAN, C.F. ... et al, 2019. Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces. Mathematische Zeitschrift, doi:10.1007/s00209-019-02279-9.

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Springer © The Authors

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

Acceptance date

27/02/2019

Publication date

2019-04-03

Copyright date

2020

Notes

This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

ISSN

0025-5874

eISSN

1432-1823

Language

en

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