Geodesic
Birational automorphisms of a~class of varieties fibred into cubic surfaces
Izvestiya. Mathematics , Tome 66 (2002) no. 1, pp. 201-222

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We investigate the properties of a variety $V$ that is a divisor of bidegree $(2,3)$ in $\mathbb P^1\times\mathbb P^3$. We calculate the group of its birational automorphisms and prove that $V$ admits no conic bundle structure and is not rational. 
@article{IM2_2002_66_1_a8,
     author = {I. V. Sobolev},
     title = {Birational automorphisms of a~class of varieties fibred into cubic surfaces},
     journal = {Izvestiya. Mathematics },
     pages = {201--222},
     publisher = {mathdoc},
     volume = {66},
     number = {1},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_1_a8/}
}
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I. V. Sobolev. Birational automorphisms of a~class of varieties fibred into cubic surfaces. Izvestiya. Mathematics , Tome 66 (2002) no. 1, pp. 201-222. http://geodesic.mathdoc.fr/item/IM2_2002_66_1_a8/