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Invariants in equivariant birational geometry

Andrew Kresch, Yuri Tschinkel

Abstract

We discuss invariants in equivariant birational geometry.

Invariants in equivariant birational geometry

Abstract

We discuss invariants in equivariant birational geometry.
Paper Structure (32 sections, 22 theorems, 189 equations)

This paper contains 32 sections, 22 theorems, 189 equations.

Table of Contents

  1. Introduction
  2. Key ideas
  3. Equivariant birational geometry
  4. Background
  5. Cremona group
  6. Equivariant birational rigidity
  7. Stacks
  8. No-name lemma
  9. Obstructions in $G$-equivariant geometry
  10. Dimension
  11. Fixed points
  12. Determinant
  13. Cohomology
  14. Coniveau filtrations
  15. Intermediate Jacobians
  16. ...and 17 more sections

Key Result

Lemma 3.1

Let $X$ be a $G$-variety, where the $G$-action on $X$ is generically free. Let $E\to X$ be a $G$-vector bundle of rank $n\ge 1$. Then, letting $G$ act trivially on ${\mathbb P}^{n-1}$ we have compatibly with the projection maps to $X$.

Theorems & Definitions (54)

  • Lemma 3.1: No-name lemma, projective bundle version
  • proof
  • Corollary 3.2
  • Corollary 3.3
  • Proposition 4.1: RYessential
  • Example 4.2
  • Proposition 4.3: RYinvariant
  • Remark 4.4
  • Proposition 4.5
  • Remark 4.6
  • ...and 44 more