Hyperelliptic curves with prescribed p-torsion

By Darren B. Glass, R. Pries. 2004

61 citations recorded by the source corpus.

In this paper, we show that there exist families of curves (defined over an algebraically closed field k of characteristic p>2) whose Jacobians have interesting p-torsion. For example, for every 0≤f≤g, we find the dimension of the locus of hyperelliptic curves of genus g with p-rank at most f. We also produce families of curves so that the p-torsion of the Jacobian of each fibre contains multiple copies of the group scheme αp. The method is to study curves which admit an action by (ℤ/2)n so that the quotient is a projective line. As a result, some of these families intersect the hyperelliptic locus .

Subfields: Computational Theory and Mathematics, Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/51d3359181811deafc2d1e318c403c2698ff69dc

Citations in the corpus

• Abelian varieties isogenous to a Jacobian (2012, unknown): “In [ 4 ] it is shown that components of the intersection of Vg,f with the hyperelliptic locus all have dimension equal to g − 1+ f (i.e.”