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      Counting rational points on a certain 3-parameter family of K3 surfaces

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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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          Journal
          14 December 2019
          Article
          1912.06951
          ffbc4269-96aa-466e-bc6b-471d8cf6774f

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          25 pages, 2 figures
          math.AG math.NT

          Geometry & Topology,Number theory
          Geometry & Topology, Number theory

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