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: X → 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): G(x1, x2) of degree m, whose normal closure has Galois group Am. © Foundation Compositio Mathematica 2006.

Brivio, S., Pirola, G. (2006). Alternating groups and rational functions on surfaces. COMPOSITIO MATHEMATICA, 142(2), 409-421 [10.1112/S0010437X05001715].

Alternating groups and rational functions on surfaces

Brivio, S;
2006

Abstract

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: X → 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): G(x1, x2) of degree m, whose normal closure has Galois group Am. © Foundation Compositio Mathematica 2006.
Articolo in rivista - Articolo scientifico
Alternating group; Monodromy group; Rational functions; Surfaces
English
2006
142
2
409
421
none
Brivio, S., Pirola, G. (2006). Alternating groups and rational functions on surfaces. COMPOSITIO MATHEMATICA, 142(2), 409-421 [10.1112/S0010437X05001715].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/254334
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