G-Fano threefolds, I

TL;DR

This paper classifies certain symmetric Fano threefolds with specific singularities and divisibility properties, expanding the known examples of highly symmetric Fano 3-folds.

Contribution

It provides a classification of G-Fano threefolds with particular singularities and symmetry conditions, introducing new examples with rich symmetry groups.

Findings

Identified numerous examples of G-Fano threefolds with specific properties.

Established classification criteria for Fano threefolds with terminal singularities and divisibility conditions.

Demonstrated the existence of many symmetric Fano 3-folds under the given assumptions.

Abstract

We classify Fano threefolds with only terminal singularities whose canonical class is Cartier and divisible by 2, and 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 $G$. In particular, we find a lot of examples of Fano 3-folds with "many" symmetries.