On flexibility of affine factorial varieties

TL;DR

This paper establishes a criterion for factoriality in affine varieties called suspensions, enabling the construction of numerous flexible affine factorial varieties, including a unique example of a homogeneous affine factorial 3-fold not arising from an algebraic group.

Contribution

It introduces a new criterion for factoriality of suspensions and constructs novel examples of flexible affine factorial varieties, including a distinctive 3-fold.

Findings

Criterion for factoriality of suspensions established

Many new examples of flexible affine factorial varieties constructed

Identified a homogeneous affine factorial 3-fold not from an algebraic group

Abstract

We give a criterion of factoriality of a suspension. This allows to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine factorial 3-fold that is not a homogeneous space of an algebraic group.