Rationality of Three-Dimensional Quotients by Monomial Actions

Details Rationality of Three-Dimensional Quotients by Monomial Actions Rationality of Three-Dimensional Quotients by Monomial Actions

2009-10-07

arxiv.org/abs/0910.1148v1

Mathematics

Algebraic Geometry

Scientific paper

Let $G$ be a finite 2-group and $K$ be a field satisfying that (i)
$\fn{char}K\ne 2$, and (ii) $\sqrt{a}\in K$ for any $a\in K$. If $G$ acts on
the rational function field $K(x,y,z)$ by monomial $K$-automorphisms, then the
fixed field $K(x,y,z)^G$ is rational (= purely transcendental) over $K$.
Applications of this theorem will be given.

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