Actions on the Picard group of smooth Fano threefolds

TL;DR

This paper classifies how automorphisms of smooth Fano threefolds act on their Picard groups and explores the first group cohomology of the Picard group across different families.

Contribution

It provides a classification of automorphism actions on Picard groups and analyzes the first group cohomology for families of smooth Fano threefolds.

Findings

Classification of automorphism group actions on Picard groups.

Analysis of first group cohomology in Fano threefold families.

Insights into symmetry and deformation properties of 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.