Toric $G$-Fano Threefolds

TL;DR

This paper classifies certain toric Fano threefolds with terminal singularities based on the rank of their G-invariant class group, advancing understanding of their automorphism group actions.

Contribution

It provides a classification of toric G-Fano threefolds with specific singularities and invariant class group properties, a novel contribution in algebraic geometry.

Findings

Classification of toric G-Fano threefolds with terminal singularities

Identification of conditions on the G-invariant class group

Insights into automorphism group actions on these varieties

Abstract

We classify toric Fano threefolds having at worst terminal singularities such that a rank of a $G$-invariant part of a class group equals one, where $G$ is a group acting on the variety by automorphisms.