Geodesic
Birational automorphisms of a class of varieties fibred into cubic surfaces
Izvestiya. Mathematics, Tome 66 (2002) no. 1, pp. 201-222 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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