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- W2809953229 abstract "Let $k$ be a field, $x_1, dots, x_n$ be independent variables and $L_n = k(x_1, dots, x_n)$. The symmetric group $Sigma_n$ acts on $L_n$ by permuting variables, and projective linear group $text{PGL}_2$ acts by [ begin{pmatrix} a & b c & d end{pmatrix} colon x_i mapsto frac{a x_i + b}{c x_i + d} ] for each $i = 1, ldots, n$. The fixed field $L_n^{text{PGL}_2}$ is called the field of cross-ratios. Given a subgroup $S subset Sigma_n$, H. Tsunogai asked whether $L_n^S$ rational over $K_n^S$. When $n geqslant 5$ second author has shown that $L_n^S$ is rational over $K_n^S$ if and only if $S$ has an orbit of odd order in ${ 1, dots, n }$. In this paper we answer Tsunogai's question for $n leqslant 4$." @default.
- W2809953229 created "2018-07-10" @default.
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- W2809953229 date "2020-07-11" @default.
- W2809953229 modified "2023-09-27" @default.
- W2809953229 title "On a rationality problem for fields of cross-ratios II" @default.
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