Mathematics – Algebraic Geometry
Scientific paper
2009-02-26
Mathematics
Algebraic Geometry
Slight reorganization, improved results for p-rank zero locus
Scientific paper
We prove results about the intersection of the p-rank strata and the boundary of the moduli space of hyperelliptic curves in characteristic p > 2. Using this, we prove that the Z/\ell-monodromy of every irreducible component of the stratum H_g^f of hyperelliptic curves of genus g and p-rank f is the symplectic group Sp_{2g}(Z/\ell) if g > 2, f > 0 and \ell is an odd prime distinct from p. These results yield applications about the generic behavior of hyperelliptic curves of given genus and p-rank. The first application is that a generic hyperelliptic curve of genus g > 2 and p-rank 0 is not supersingular. Other applications are about absolutely simple Jacobians and the generic behavior of class groups and zeta functions of hyperelliptic curves of given genus and $p$-rank over finite fields.
Achter Jeff
Pries Rachel
No associations
LandOfFree
The p-rank strata of the moduli space of hyperelliptic curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The p-rank strata of the moduli space of hyperelliptic curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The p-rank strata of the moduli space of hyperelliptic curves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-254738