Kummer sandwiches and Greene–Plesser construction

In the context of K3 mirror symmetry, the Greene–Plesser orbifolding method constructs a family of K3 surfaces, the mirror of quartic hypersurfaces in P3, starting from a special one-parameter family of K3 varieties known as the quartic Dwork pencil. We show that certain K3 double covers obtained fr...

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Bibliographic Details
Published in:Journal of geometry and physics 2020-08, Vol.154, p.103718, Article 103718
Main Authors: Braeger, Noah, Malmendier, Andreas, Sung, Yih
Format: Article
Language:English
Subjects:
Greene–Plesser orbifolding method
K3 surfaces
Kummer sandwich theorem
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Summary:In the context of K3 mirror symmetry, the Greene–Plesser orbifolding method constructs a family of K3 surfaces, the mirror of quartic hypersurfaces in P3, 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.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2020.103718