Character varieties of free groups are Gorenstein but not always factorial

Sean Lawton; Christopher Manon

doi:10.1016/j.jalgebra.2016.01.044

Character varieties of free groups are Gorenstein but not always factorial

Sean Lawton
, Christopher Manon

Mathematics

Producción científica: Article › revisión exhaustiva

6 Citas (Scopus)

Resumen

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

Idioma original	English
Páginas (desde-hasta)	278-293
Número de páginas	16
Publicación	Journal of Algebra
Volumen	456
DOI	https://doi.org/10.1016/j.jalgebra.2016.01.044
Estado	Published - jun 15 2016

Nota bibliográfica

Publisher Copyright:
© 2016 Elsevier Inc.

Financiación

We thank both Brian Conrad and Vladimir Popov for giving references and comments concerning Lemma 2.1 ; this was extremely helpful. We also thank Neil Epstein for several useful discussions on factorial rings. Manon was supported by a grant from the National Science Foundation (DMS # 1500966 ). Lawton was partially supported by grants from the Simons Foundation (Collaboration # 245642 ) and the National Science Foundation (DMS # 1309376 ). Additionally, Lawton acknowledges support by the National Science Foundation under Grant No. 0932078000 while in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2015 semester. Finally, we thank an anonymous referee for helpful references.

Financiadores	Número del financiador
National Science Foundation (NSF)
Directorate for Mathematical and Physical Sciences	1309376
Division of Mathematical Sciences	1500966
Simons Foundation	245642, 0932078000

ASJC Scopus subject areas

Algebra and Number Theory

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title = "Character varieties of free groups are Gorenstein but not always factorial",

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 DGg,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.",

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AU - Manon, Christopher

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AB - 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 DGg,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.

KW - Character variety

KW - Free group

KW - Gorenstein

KW - Moduli space

KW - Reductive

KW - UFD

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VL - 456

SP - 278

EP - 293

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Character varieties of free groups are Gorenstein but not always factorial

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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