Geodesic
Biregular and birational geometry of quartic double solids with 15 nodes
Izvestiya. Mathematics , Tome 83 (2019) no. 3, pp. 415-423

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Three-dimensional del Pezzo varieties of degree $2$ are double covers of $\mathbb{P}^{3}$ branched in a quartic. We prove that if a del Pezzo variety of degree $2$ has exactly $15$ nodes, then the corresponding quartic is a hyperplane section of the Igusa quartic or, equivalently, all such del Pezzo varieties are members of a particular linear system on the Coble fourfold. Their automorphism groups are induced from the automorphism group of the Coble fourfold. We also classify all birationally rigid varieties of this type.
Keywords: del Pezzo varieties, automorphism groups, birational rigidity. 
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     author = {A. Avilov},
     title = {Biregular and birational geometry of quartic double solids with 15 nodes},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_3_a1/}
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A. Avilov. Biregular and birational geometry of quartic double solids with 15 nodes. Izvestiya. Mathematics , Tome 83 (2019) no. 3, pp. 415-423. http://geodesic.mathdoc.fr/item/IM2_2019_83_3_a1/