Rationality of Three-Dimensional Quotients by Monomial Actions
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2009
- DOI:
- 10.48550/arXiv.0910.1148
- arXiv:
- arXiv:0910.1148
- Bibcode:
- 2009arXiv0910.1148K
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Commutative Algebra;
- 14E08;
- 13A50