Actions on the Picard group of smooth Fano threefolds

Abstract

We classify the possible images of the action of the group of automorphisms of a smooth Fano threefold on its Picard group. We also study the first group cohomology of the Picard group for families of smooth Fano threefolds.

28 pages; revised version. The arguments for families 3.9 and 4.2 have been strengthened to determine when the previously obtained upper bounds on $\mathrm{AutP}(X)$ are realized. Some other arguments have been refined, and minor corrections have been made to incorporate the referee's comments