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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Projective isomonodromy and Galois groups


Authors: Claude Mitschi and Michael F. Singer
Journal: Proc. Amer. Math. Soc. 141 (2013), 605-617
MSC (2010): Primary 34M56, 12H05, 34M55
Published electronically: June 25, 2012
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Abstract: In this article we introduce the notion of projective isomonodromy, which is a special type of monodromy-evolving deformation of linear differential equations, based on the example of the Darboux-Halphen equation. We give an algebraic condition for a parameterized linear differential equation to be projectively isomonodromic, in terms of the derived group of its parameterized Picard-Vessiot group.


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Additional Information

Claude Mitschi
Affiliation: Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: mitschi@math.unistra.fr

Michael F. Singer
Affiliation: Department of Mathematics, North Carolina State University, Box 8205, Raleigh, North Carolina 27695-8205
Email: singer@math.ncsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11499-6
PII: S 0002-9939(2012)11499-6
Received by editor(s): February 9, 2010
Received by editor(s) in revised form: July 6, 2011
Published electronically: June 25, 2012
Additional Notes: The second author was partially supported by NSF Grants CCF-0634123 and CCF-1017217. He would also like to thank the Institut de Recherche Mathématique Avancée, Université de Strasbourg et C.N.R.S., for its hospitality and support during the preparation of this paper.
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.