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- W4300104789 abstract "Let $Bbbk$ be any field of characteristic zero, $X$ be a del Pezzo surface of degree~$2$ and $G$ be a group acting on $X$. In this paper we study $Bbbk$-rationality questions for the quotient surface $X / G$. If there are no smooth $Bbbk$-points on $X / G$ then $X / G$ is obviously non-$Bbbk$-rational. Assume that the set of smooth $Bbbk$-points on the quotient is not empty. We find a list of groups, such that the quotient surface can be non-$Bbbk$-rational. For these groups we construct examples of both $Bbbk$-rational and non-$Bbbk$-rational quotients of both $Bbbk$-rational and non-$Bbbk$-rational del Pezzo surfaces of degree $2$ such that the $G$-invariant Picard number of $X$ is $1$. For all other groups we show that the quotient $X / G$ is always $Bbbk$-rational." @default.
- W4300104789 created "2022-10-03" @default.
- W4300104789 creator A5030376370 @default.
- W4300104789 date "2017-09-06" @default.
- W4300104789 modified "2023-10-16" @default.
- W4300104789 title "Quotients of del Pezzo surfaces of degree 2" @default.
- W4300104789 doi "https://doi.org/10.48550/arxiv.1709.02006" @default.
- W4300104789 hasPublicationYear "2017" @default.
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