Geodesic
Equations of $G$-minimal conic bundles with degree $4$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 39-42

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The first nontrivial case of relatively $G$-minimal conic bundles being $G$-minimal is considered. The number $r$ of singular fibers equals $4$. Classification gives explicit equations of minimal conic bundles $(S,G)$ and an explicit action of the group $G$ on the Picard group $\operatorname{Pic}(S)$ and on the surface $S$. 
@article{VMUMM_2010_2_a6,
     author = {V. I. Tsygankov},
     title = {Equations of $G$-minimal conic bundles with degree $4$},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {39--42},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a6/}
}
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V. I. Tsygankov. Equations of $G$-minimal conic bundles with degree $4$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 39-42. http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a6/