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Rationality of forms of $\overline{\mathcal M}_{0,n}$

Brendan Hassett, Yuri Tschinkel, Zhijia Zhang

Abstract

We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.

Rationality of forms of $\overline{\mathcal M}_{0,n}$

Abstract

We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.
Paper Structure (6 sections, 22 theorems, 172 equations)

This paper contains 6 sections, 22 theorems, 172 equations.

Table of Contents

  1. Introduction
  2. ${\mathfrak S}_n$-equivariant geometry
  3. Rationality constructions
  4. Stable linearizability via torsors
  5. Computing cohomology
  6. Three-dimensional case

Key Result

Theorem 1

For every even $n\ge 6$ there exists a subgroup $G=C_2^2\subset {\mathfrak S}_n$ such that In particular,

Theorems & Definitions (43)

  • Theorem 1: Corollary \ref{['coro:linear']} and Theorem \ref{['thm:biquad']}
  • Proposition 2
  • proof
  • Lemma 3
  • Proposition 4
  • proof
  • Example 5
  • Proposition 6
  • Proposition 7
  • Proposition 8
  • ...and 33 more