Rationality of quotients by linear actions of affine groups

Fedor Bogomolov, Christian Böhning, Hans Christian Graf von Bothmer

Research output: Contribution to journalArticlepeer-review

Abstract

Let G = SLn(ℂ) ⋉ ℂn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).

Original languageEnglish (US)
Pages (from-to)1521-1532
Number of pages12
JournalScience China Mathematics
Volume54
Issue number8
DOIs
StatePublished - Aug 2011

Keywords

  • affine groups
  • linear group quotients
  • rationality

ASJC Scopus subject areas

  • Mathematics(all)

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