Automorphism groups and linearizability of rational Fano conic bundle threefolds

Abstract: We generalize the equivariant intermediate Jacobian torsor obstruction over $\mathbb{C}$ to algebraically closed fields of characteristic zero. It is an obstruction to the (projective) linearizability problem of finite group actions on threefolds. In addition, we calculate automorphism groups of general smooth Fano threefolds of No. 2.18. As an application, we prove that a general smooth Fano threefold X of No. 2.18 is linearizable for its automorphism group.