On a~double cone over a~Veronese surface
Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 421-438

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We study the birational geometry of a Fano threefold that is a double covering of a cone over a Veronese surface with ramification at a non-singular section by a cubic. In particular, we consider the set of Mori structures and possible types of maximal singularities of linear systems.
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     author = {M. M. Grinenko},
     title = {On a~double cone over {a~Veronese} surface},
     journal = {Izvestiya. Mathematics },
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M. M. Grinenko. On a~double cone over a~Veronese surface. Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 421-438. http://geodesic.mathdoc.fr/item/IM2_2003_67_3_a1/