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- W4301372261 abstract "Given a smooth plane curve $overline{C}$ of genus $ggeq 3$ over an algebraically closed field $overline{k}$, a field $Lsubseteqoverline{k}$ is said to be a emph{plane model-field of definition for $overline{C}$} if $L$ is a field of definition for $overline{C}$, i.e. $exists$ a smooth curve $C'$ defined over $L$ where $C'times_Loverline{k}cong overline{C}$, and such that $C'$ is $L$-isomorphic to a non-singular plane model $F(X,Y,Z)=0$ in $mathbb{P}^2_{L}$. {In this short note, we construct a smooth plane curve $overline{C}$ over $overline{mathbb{Q}}$, such that the field of moduli of $overline{C}$ is not a field of definition for $overline{C}$, and also fields of definition do not coincide with plane model-fields of definition for $overline{C}$.} As far as we know, this is the first example in the literature with the above property, since this phenomenon does not occur for hyperelliptic curves, replacing plane model-fields of definition with the so-called hyperelliptic model-fields of definition." @default.
- W4301372261 created "2022-10-05" @default.
- W4301372261 creator A5011326339 @default.
- W4301372261 creator A5059041901 @default.
- W4301372261 date "2017-05-02" @default.
- W4301372261 modified "2023-10-16" @default.
- W4301372261 title "Plane model-fields of definition, fields of definition, the field of moduli of smooth plane curves" @default.
- W4301372261 doi "https://doi.org/10.48550/arxiv.1705.00901" @default.
- W4301372261 hasPublicationYear "2017" @default.
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