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Equivariant geometry of low-dimensional quadrics

Brendan Hassett, Yuri Tschinkel

Abstract

We provide new stable linearizability constructions for regular actions of finite groups on homogeneous spaces and low-dimensional quadrics.

Equivariant geometry of low-dimensional quadrics

Abstract

We provide new stable linearizability constructions for regular actions of finite groups on homogeneous spaces and low-dimensional quadrics.

Paper Structure

This paper contains 14 sections, 21 theorems, 79 equations.

Table of Contents

  1. Introduction
  2. Groups actions, twists, and rationality
  3. Notions of linearizability
  4. Projective bundles
  5. Notions of versality
  6. Quadrics and isotropic subspaces
  7. Flag varieties and special groups
  8. Quadric hypersurfaces
  9. Arbitrary dimensions
  10. Pfaffian constructions
  11. Springer-type results
  12. Quadric threefolds
  13. Quadric fourfolds
  14. Applications to threefolds

Key Result

Proposition 2.3

Let $G$ and $H$ be finite groups acting generically freely on $\mathbb P(V)$ and $\mathbb P(W)$ respectively. Then the induced action of $G \times H$ on $\mathbb P(V) \times \mathbb P(W)$ is stably linearizable.

Theorems & Definitions (46)

  • Remark 2.1
  • Example 2.2
  • Proposition 2.3
  • proof
  • Example 2.4
  • Remark 2.5
  • Remark 2.6
  • Definition 3.1
  • Proposition 3.2
  • proof
  • ...and 36 more