266 research outputs found
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
, 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 -isogenies of the
underlying abelian surface.Comment: 27 pages; minor typos corrected in version
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