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
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

DOI: https://doi.org/10.1090/jag/668
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.

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