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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Symmetric cubic surfaces and $\mathbf {G}_2$ character varieties


Authors: Philip Boalch and Robert Paluba
Journal: J. Algebraic Geom. 25 (2016), 607-631
DOI: https://doi.org/10.1090/jag/668
Published electronically: April 6, 2016
MathSciNet review: 3533182
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Abstract | References | Additional Information

Abstract: We will consider a two dimensional “symmetric” subfamily of the four dimensional family of Fricke cubic surfaces. The main result is that such symmetric cubic surfaces arise as character varieties for the exceptional group of type $G_2$. Further, this symmetric family will be related to the fixed points of the triality automorphism of $\operatorname {Spin}(8)$, and an example involving the finite simple group of order $6048$ inside $G_2$ will be considered.


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Philip Boalch
Affiliation: Laboratoire de Mathématiques d’Orsay (CNRS UMR 8628), Bâtiment 425, Université Paris-Sud, 91405 Orsay, France
MR Author ID: 686227
Email: philip.boalch@math.u-psud.fr

Robert Paluba
Affiliation: Laboratoire de Mathématiques d’Orsay (CNRS UMR 8628), Bâtiment 425, Université Paris-Sud, 91405 Orsay, France
Email: robert.paluba@math.u-psud.fr

Received by editor(s): June 2, 2013
Received by editor(s) in revised form: July 9, 2014, and September 27, 2014
Published electronically: April 6, 2016
Additional Notes: The first-named author was partially supported by ANR grants 08-BLAN-0317-01/02, 09-JCJC-0102-01, 13-BS01-0001-01, and 13-IS01-0001-01/02
Article copyright: © Copyright 2016 University Press, Inc.