Character varieties of free groups are Gorenstein but not always factorial

Sean Lawton, Christopher Manon

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Fix a rank g free group Fg and a connected reductive complex algebraic group G. Let X(Fg,G) be the G-character variety of Fg. When the derived subgroup DG<G is simply connected we show that X(Fg,G) is factorial (which implies it is Gorenstein), and provide examples to show that when DG is not simply connected X(Fg,G) need not even be locally factorial. Despite the general failure of factoriality of these moduli spaces, using different methods, we show that X(Fg,G) is always Gorenstein.

Original languageEnglish
Pages (from-to)278-293
Number of pages16
JournalJournal of Algebra
Volume456
DOIs
StatePublished - Jun 15 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

  • Character variety
  • Free group
  • Gorenstein
  • Moduli space
  • Reductive
  • UFD

ASJC Scopus subject areas

  • Algebra and Number Theory

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