Elliptic Delsarte surfaces

PhD ceremony: Mr. B.L. Heijne, 14.30 uur, Aula Academiegebouw, Broerstraat 5, Groningen

Dissertation: Elliptic Delsarte surfaces

Promotor(s): prof. J. Top

Faculty: Mathematics and Natural Sciences

An elliptic curve is a curve on which an addition is defined. An elliptic surface is a surface that consists of infinitely many elliptic curves. The addition on these curves gives an addition on the so called group of sections of this surface. The size of this group of sections can be expressed with a number, the rank.

In this thesis we determine that largest possible rank that can be attained for a specific family of elliptic surfaces. This family is the family of elliptic Delsarte surfaces. By subdividing this family into several subfamilies we are able to determine the maximal rank of this entire family. This turns out to be 68. Thereafter the group of sections of elliptic Delsarte surfaces is described as explicitly as possible.