Re: Hyperelliptic curves examples!!

From: JHS (jhsntru_at_yahoo.com)
Date: 03/02/04 

Date: 2 Mar 2004 05:09:33 -0800

Timothy Murphy <tim@birdsnest.maths.tcd.ie> wrote in message news:<WXQ0c.5211$rb.63744@news.indigo.ie>...
> OP wrote:
>
> > I would like to some examples of HyperElliptic Curves (HEC) and
> > supersingular curves too.. of different genus along wiht the points
> > for different fields.. so I can calculate the divisors and test the
> > arithmetic algorithm that I have written. Can some one give me
> > references as to where I can find them.
>
> I thought the term "supersingular" only applied to elliptic curves.
> (so of genus 1).
> What does it mean to say that a general curve is supersingular?

"Supersingular" applies to abelian varieties of any dimension, so
possibly the OP wants curves whose Jacobian varieties are
supersingular. But I suspect that the OP meant to say "superelliptic",
which is Serge Lang's term for curves of the form y^n=f(x). In more
prosaic terms, these are cyclic covers of the projective line.

JS