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arXiv · 1912.06951

Kummer sandwiches and Greene-Plesser construction

Noah Braeger·Andreas Malmendier·Yih Sung
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Abstract

In the context of K3 mirror symmetry, the Greene-Plesser orbifolding method constructs a family of K3 surfaces, the mirror of quartic hypersurfaces in $\mathbb{P}^3$, starting from a special one-parameter family of K3 varieties known as the quartic Dwork pencil. We show that certain K3 double covers obtained from the three-parameter family of quartic Kummer surfaces associated with a principally polarized abelian surface generalize the relation of the Dwork pencil and the quartic mirror family. Moreover, for the three-parameter family we compute a formula for the rational point-count of its generic member and derive its transformation behavior with respect to $(2,2)$-isogenies of the underlying abelian surface.

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Noah Braeger, Andreas Malmendier, Yih Sung. 2019-12-14. Kummer sandwiches and Greene-Plesser construction. https://doi.org/10.1016/j.geomphys.2020.103718

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