International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn053, 25 pages, doi:10.1093/imrn/rnn053
published on
June 13, 2008
© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org
Monodromy of the p-Rank Strata of the Moduli Space of Curves
Jeffrey D. Achter and
Rachel Pries
Department of Mathematics, Colorado State University, Fort Collins, CO 80523
Correspondence: Correspondence to be sent to: pries{at}math.colostate.edu
We determine the 
-monodromy and 
-monodromy of every irreducible component of the stratum 
of curves of genus g and p-rank f in characteristic p. In particular, we prove that the 
-monodromy of every component of 
is the symplectic group 
if 
and if 
is a prime distinct from p. The method involves results on the intersection of 
with the boundary of 
. We give applications to the generic behavior of automorphism groups, Jacobians, class groups, and zeta functions of curves of given genus and p-rank.
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