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- W4300706670 abstract "We classify all rational maps $H in K(x)^n$ for which ${rm trdeg}_K K(tH_1,tH_2,ldots,tH_n) le 2$, where $K$ is any field and $t$ is another indeterminate. Furthermore, we classify all such maps for which additionally $JH cdot H = {rm tr} JH cdot H$ (where $JH$ is the Jacobian matrix of $H$), i.e. $$ sum_{i=1}^n H_i frac{partial}{partial x_i} H_k = sum_{i=1}^n H_k frac{partial}{partial x_i} H_i $$ for all $k le n$. This generalizes a theorem of Paul Gordan and Max Nother, in which both sides and the characteristic of $K$ are assumed to be zero. Besides this, we use some of our tools to obtain several results about $K$-subalgebras $R$ of $K(x)$ for which ${rm trdeg}_K L = 1$, where $L$ is the fraction field of $R$. We start with some observations about to what extent, Luroth's theorem can be generalized." @default.
- W4300706670 created "2022-10-04" @default.
- W4300706670 creator A5007201904 @default.
- W4300706670 date "2015-01-24" @default.
- W4300706670 modified "2023-09-29" @default.
- W4300706670 title "Rational maps $H$ for which $K(tH)$ has transcendence degree 2 over $K$" @default.
- W4300706670 doi "https://doi.org/10.48550/arxiv.1501.06046" @default.
- W4300706670 hasPublicationYear "2015" @default.
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