Families of supersingular curves in characteristic 2
Abstract
This paper determines the normal forms of hyperelliptic supersingular curves of genus g over an algebraically closed field F of characteristic 2 for 0 < g< 9. We also show that every hyperelliptic supersingular curve of genus 9 over F has an equation y^2-y=x^19+c^8x^9+c^3x for some c in F_2bar. The paper determines the dimensions of the open locus of hyperelliptic supersingular curves of genus g < 10 over F_2bar.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- December 2001
- DOI:
- 10.48550/arXiv.math/0112086
- arXiv:
- arXiv:math/0112086
- Bibcode:
- 2001math.....12086S
- Keywords:
-
- Algebraic Geometry;
- Number Theory
- E-Print:
- 11 pages, LaTeX