Automorphism groups and linearizability of rational Fano conic bundle threefolds

TL;DR

This paper extends the equivariant intermediate Jacobian torsor obstruction to characteristic zero fields, analyzes automorphism groups of certain Fano threefolds, and proves linearizability for a general case.

Contribution

It introduces a generalized obstruction for linearizability over algebraically closed fields and computes automorphism groups for specific Fano threefolds, establishing linearizability in a new case.

Findings

Obstruction generalized to characteristic zero fields

Automorphism groups of general smooth Fano threefolds computed

General smooth Fano threefolds of No. 2.18 are proven to be linearizable

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.