Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-24T13:23:26.538Z Has data issue: false hasContentIssue false

Alternating groups and rational functions on surfaces

Published online by Cambridge University Press:  13 March 2006

Sonia Brivio
Affiliation:
Dipartimento di Matematica, Universitá di Pavia, via Ferrata 1, 27100 Pavia, [email protected]
Gian Pietro Pirola
Affiliation:
Dipartimento di Matematica, Universitá di Pavia, via Ferrata 1, 27100 Pavia, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be a smooth complex projective surface and let C(X) denote the field of rational functions on X. In this paper, we prove that for any m > M(X), there exists a rational dominant map $f \colon X \to Y$, which is generically finite of degree m, into a complex rational ruled surface Y, whose monodromy is the alternating group Am. This gives a finite algebraic extension C(X): C(x1, x2) of degree m, whose normal closure has Galois group Am.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2006