Smooth Fano 3-folds satisfying Condition (A)

TL;DR

This paper classifies smooth Fano 3-folds that satisfy a specific fixed point condition for all finite abelian subgroups of their automorphism groups, advancing understanding of their symmetry properties.

Contribution

It provides a complete classification of smooth Fano 3-folds satisfying Condition (A), a property related to automorphism group actions.

Findings

Complete classification of smooth Fano 3-folds with Condition (A)

Identification of automorphism group fixed point properties

Insights into symmetry constraints of Fano 3-folds

Abstract

A smooth variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We classify smooth Fano 3-folds that satisfy Condition (A).