60 research outputs found

    The Maximal Rank of Elliptic Delsarte Surfaces

    Full text link
    Shioda described in his article from 1986 a method to compute the Lefschetz number of a Delsarte surface. In one of his examples he uses this method to compute the rank of an elliptic curve over k(t). In this article we find all elliptic curves over k(t) for which his method is applicable. For each of these curves we also compute the Mordell-Weil rank

    Zeta Functions of Monomial Deformations of Delsarte Hypersurfaces

    Get PDF
    Let XλX_\lambda and XλX_\lambda' be monomial deformations of two Delsarte hypersurfaces in weighted projective spaces. In this paper we give a sufficient condition so that their zeta functions have a common factor. This generalises results by Doran, Kelly, Salerno, Sperber, Voight and Whitcher [arXiv:1612.09249], where they showed this for a particular monomial deformation of a Calabi-Yau invertible polynomial. It turns out that our factor can be of higher degree than the factor found in [arXiv:1612.09249]

    Elliptic delsarte surfaces

    Get PDF
    corecore