60 research outputs found
The Maximal Rank of Elliptic Delsarte Surfaces
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
Let and 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]
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