Automorphisms of threefolds that can be represented as an intersection of two quadrics

Abstract

We prove that any -del Pezzo threefold of degree , except for a one-parameter family and four distinguished cases, can be equivariantly reconstructed to the projective space , a quadric , a -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 subgroup of its automorphism group. Bibliography: 15 titles.