Geodesic
Automorphisms of threefolds that can be represented as an intersection of two quadrics
Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 315-330

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We prove that any $G$-del Pezzo threefold of degree $4$, except for a one-parameter family and four distinguished cases, can be equivariantly reconstructed to the projective space $\mathbb P^3$, a quadric $Q\subset\mathbb P^4$, a $G$-conic bundle or a del Pezzo fibration. We also show that one of these four distinguished varieties is birationally rigid with respect to an index $2$ subgroup of its automorphism group. Bibliography: 15 titles.
Keywords: del Pezzo varieties, automorphism groups, birational rigidity. 
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A. Avilov. Automorphisms of threefolds that can be represented as an intersection of two quadrics. Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 315-330. http://geodesic.mathdoc.fr/item/SM_2016_207_3_a0/