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

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	278-293
Number of pages	16
Journal	Journal of Algebra
Volume	456
DOIs	https://doi.org/10.1016/j.jalgebra.2016.01.044
State	Published - 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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10.1016/j.jalgebra.2016.01.044

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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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Y1 - 2016/6/15

N2 - 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.

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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SN - 0021-8693

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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