G-Fano threefolds, II

TL;DR

This paper classifies a specific class of Gorenstein Fano threefolds with certain symmetry and divisor class group properties, expanding the understanding of their structure and classification.

Contribution

It provides a classification of G-Fano threefolds with Picard number > 1 under specific symmetry and divisor class group conditions.

Findings

Complete classification of G-Fano threefolds under given conditions

Identification of structural properties related to group actions

Extension of known classifications in Fano geometry

Abstract

We classify Fano threefolds with only Gorenstein terminal singularities and Picard number greater than 1 satisfying an additional assumption that the $G$-invariant part of the Weil divisor class group is of rank 1 with respect to an action of some group $G$.