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On flexibility of affine factorial varieties

Ivan Arzhantsev, Kirill Shakhmatov

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.

On flexibility of affine factorial varieties

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.

Paper Structure

This paper contains 5 sections, 17 theorems, 47 equations.

Table of Contents

  1. Basic lemmas
  2. A criterion of factoriality
  3. Homogeneous varieties vs homogeneous spaces
  4. The divisor class group
  5. A remark on suspensions

Key Result

Lemma 1

For a nonzero $f$, the ring $S$ is a domain if and only if $R$ is a domain.

Theorems & Definitions (32)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • ...and 22 more