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- W2555446926 abstract "In this thesis we study questions from a branch of mathematics called arithmetic geometry: the research on number theoretic properties of geometric objects described by algebraic equations. The first topic concerns so-called maximal curves. A curve is described by an algebraic equation in two unknowns. Solutions to the equation are called points. In our case the curve has only finitely many points. The work of Hasse, Weil and Serre provides bounds on the number of points. For a maximal curve the number of points is equal to this upper bound. We study constructions of maximal curves such that the curve remains the same, but the points are considered over varying fields. The second topic is on the Hesse pencil. This is a set of (elliptic) curves that have nine flex points in common. The set is provided with a geometric structure. We show that the structure on the flex points determines whether or not a given elliptic curve belongs to the Hesse pencil. The last topic is related to a curve introduced by Mestre. We split the so-called Jacobian variety of this curve in simple factors. In doing so, we adapt methods by Faltings and by van Wamelen to new situations." @default.
- W2555446926 created "2016-11-30" @default.
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- W2555446926 date "2016-01-01" @default.
- W2555446926 modified "2023-09-27" @default.
- W2555446926 title "The arithmetic of maximal curves, the Hesse pencil and Mestre curve" @default.
- W2555446926 hasPublicationYear "2016" @default.
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