Tuijp, A. (2015) Hesse pencil in characteristic two. Bachelor's Thesis, Mathematics.
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Abstract
In this paper we look at flex points on elliptic curves and to what extend they characterize the curve itself. In characteristic different from two and three, there exists a certain theorem about this by A. Anema. We will show that this theorem is also true in characteristic two. First, we give a short introduction to elliptic curves, the three-torsion group and the Weil-pairing. Then, given an elliptic curve in characteristic two, we define a curve that is in some way analogous to the Hessian in other characteristics: it intersects the elliptic curve only at its flex points. We use this alternative Hessian curve to define a Hesse pencil in characteristic two. Finally, we prove the only remaining proposition in Anema's proof for which an alternative proof is needed in characteristic two.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 08:06 |
| Last Modified: | 15 Feb 2018 08:06 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/13074 |
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