Geodesic
Equations of $G$-minimal conic bundles
Sbornik. Mathematics, Tome 202 (2011) no. 11, pp. 1667-1721

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We develop a method for obtaining equations for $G$-minimal conic bundles with an arbitrary number of singular fibres. When the number of singular fibres is equal to $4$, $6$, or $7$, a detailed classification is given, which includes obtaining the equations for minimal conic bundles $(S,G)$ and an explicit indication of the action of the group $G$ on the Picard group $\operatorname{Pic}(S)$ and on the surface $S$ itself. Bibliography: 19 titles.
Keywords: Cremona group, conic bundle
Mots-clés : automorphism group. 
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     author = {V. I. Tsygankov},
     title = {Equations of $G$-minimal conic bundles},
     journal = {Sbornik. Mathematics},
     pages = {1667--1721},
     publisher = {mathdoc},
     volume = {202},
     number = {11},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_11_a5/}
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V. I. Tsygankov. Equations of $G$-minimal conic bundles. Sbornik. Mathematics, Tome 202 (2011) no. 11, pp. 1667-1721. http://geodesic.mathdoc.fr/item/SM_2011_202_11_a5/