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arXiv · 1511.08778

Calabi-Yau threefolds of type K (II): Mirror symmetry

Kenji Hashimoto·Atsushi Kanazawa
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Abstract

A Calabi-Yau threefold is called of type K if it admits an étale Galois covering by the product of a K3 surface and an elliptic curve. In our previous paper, based on Oguiso-Sakurai's fundamental work, we provide the full classification of Calabi-Yau threefolds of type K and study some basic properties thereof. In the present paper, we continue the study, investigating them from the viewpoint of mirror symmetry. It is shown that mirror symmetry relies on a duality of certain sublattices in the second cohomology of the K3 surface appearing in the minimal splitting covering. The duality may be thought of as a version of the lattice duality of the anti-symplectic involution on K3 surfaces discovered by Nikulin. Based on the duality, we obtain several results parallel to what is known for Borcea-Voisin threefolds. Along the way, we also investigate the Brauer groups of Calabi-Yau threefolds of type K.

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Kenji Hashimoto, Atsushi Kanazawa. 2016-06-20. Calabi-Yau threefolds of type K (II): Mirror symmetry. https://arxiv.org/abs/1511.08778

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