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On rings of commuting partial differential operators

Author: A. B. Zheglov
Translated by: the author
Original publication: Algebra i Analiz, tom 25 (2013), nomer 5.
Journal: St. Petersburg Math. J. 25 (2014), 775-814
MSC (2010): Primary 14D15, 14D20
Published electronically: July 18, 2014
MathSciNet review: 3184608
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Abstract | References | Similar Articles | Additional Information

Abstract: A natural generalization is given for the classification of commutative rings of ordinary differential operators, as presented by Krichever, Mumford, Mulase. The commutative rings of operators in a completed ring of partial differential operators in two variables (satisfying certain mild conditions) are classified in terms of Parshin's generalized geometric data. This classification involves a generalization of M. Sato's theory and is constructible both ways.

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Additional Information

A. B. Zheglov
Affiliation: Division of Differential Geometry and Applications, Department of Mathematics and Mechanics, Lomonosov Mascow State University, Leninskie gory, Moscow 119809, Russia

Keywords: Commuting partial differential operators; two-dimensional
Received by editor(s): August 27, 2012
Published electronically: July 18, 2014
Additional Notes: Supported by RFBR (grant no. 11-01-00145-a), by SSh (grant no. 1410.2012.1), by the National Scientific Projects (grant no. 14.740.11.0794), and by a grant of the Government of the Russian Federation for support of research projects implemented by leading scientists at Lomonosov Moscow State University under the agreement no. 11.G34.31.0054.
Article copyright: © Copyright 2014 American Mathematical Society