Alternating groups as monodromy groups in positive characteristic

Stefan Wewers and Irene I. Bouw

Vol. 222 (2005), No. 1, 185–200

DOI: 10.2140/pjm.2005.222.185

Abstract

Let X be a generic curve of genus g defined over an algebraically closed field k of characteristic p ≥ 0. We show that for n sufficiently large there exists a tame rational map f : X → ℙ_k¹ of degree n with monodromy group A_n. This generalizes a result of Magaard and Völklein to positive characteristic.

Keywords

covers, moduli of curves, positive characteristic

Mathematical Subject Classification 2000

Primary: 14H30

Milestones

Received: 1 March 2004

Revised: 5 September 2004

Accepted: 24 August 2004

Published: 1 November 2005