English

Families of supersingular curves in characteristic 2

Algebraic Geometry 2007-05-23 v1 Number Theory

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.

Keywords

Cite

@article{arxiv.math/0112086,
  title  = {Families of supersingular curves in characteristic 2},
  author = {Jasper Scholten and Hui June Zhu},
  journal= {arXiv preprint arXiv:math/0112086},
  year   = {2007}
}

Comments

11 pages, LaTeX