Fano threefolds with noncyclic torsion in the divisor class group

TL;DR

This paper investigates Fano threefolds with noncyclic torsion in their divisor class group, showing they can all be derived as quotients of other Fano threefolds, including those in weighted projective spaces.

Contribution

It classifies Fano threefolds with noncyclic torsion in the divisor class group as quotients of known Fano threefolds, expanding understanding of their structure.

Findings

All such Fano threefolds are quotients of Fano threefolds.

They include quotients of low codimension Fanos in weighted projective spaces.

Provides a classification framework for these threefolds.

Abstract

In this note we study Fano threefolds with noncyclic torsion in the divisor class group. Since they can all be obtained as quotients of Fano threefolds, we get also all examples that can be obtained as quotients of low codimension Fanos in the weighted projective space.