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. 
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/
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