Computational enumeration of superspecial curves of genus 4
Problem Setting
Let g be an integer > 1 and p a rational prime.
Given (g,p), enumerating superspecial (s.sp. for short) curves of genus g over a field K of characteristic p is a very important problem in arithmetic and algebraic geometry.
Problem Setting
Let g be an integer > 1 and p a rational prime.
Given (g,p), enumerating superspecial (s.sp. for short) curves of genus g over a field K of characteristic p is a very important problem in arithmetic and algebraic geometry.
The word "enumerate" means to list representatives (defining equations) for all isomorphism classes of those curves, where we consider isomorphisms over K, or its algebraic closure L.
Note that only finite such curves exist, up to isomorphism over L.
For the field of definition, the most important case is K=GF(p^2), since any s.sp. curve over K is L-isomorphic to that over GF(p^2).
In this page, we focus on the enumeration of s.sp. non-hyperelliptic curves of genus g=4.
The word "enumerate" means to list representatives (defining equations) for all isomorphism classes of those curves, where we consider isomorphisms over K, or its algebraic closure L.
Note that only finite such curves exist, up to isomorphism over L.
For the field of definition, the most important case is K=GF(p^2), since any s.sp. curve over K is L-isomorphic to that over GF(p^2).
In this page, we focus on the enumeration of s.sp. non-hyperelliptic curves of genus g=4.
Description pdf with tables of computational results
Description pdf with tables of computational results
The following pdf describes details of the problem, and contains tables of computational results.
The following pdf describes details of the problem, and contains tables of computational results.
- Description pdf with tables of computational results (pdf)