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Dal'nevost. Mat. Zh., 2012, Volume 12, Number 1, Pages 20–34 (Mi dvmg226)  

This article is cited in 1 scientific paper (total in 1 paper)

Baker – Akhiezer modules, Krichever sheaves, and commuting rings of partial differential operators

A. B. Zheglova, A. E. Mironovb

a M. V. Lomonosov Moscow State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: In this work we give a review of several results about commutative subrings of partial differential operators. We show that $n$-dimensional commutative ring of partial differential operators with scalar (not matrix) coefficients (with certain mild conditions) corresponds to a Baker – Akhiezer module on the spectral algebraic variety. We also show that there is a family of coherent torsion free sheaves of special type. The existence of such sheaves gives a strong restriction on the structure of the spectral variety, in particular, it is possible to find the selfintersection index of a divisor at infinity.

Key words: commuting partial differential operators, spectral varieties, Baker-Akhieser modules

Full text: PDF file (301 kB)
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UDC: 517.957
MSC: 14K25
Received: 12.10.2011

Citation: A. B. Zheglov, A. E. Mironov, “Baker – Akhiezer modules, Krichever sheaves, and commuting rings of partial differential operators”, Dal'nevost. Mat. Zh., 12:1 (2012), 20–34

Citation in format AMSBIB
\Bibitem{ZheMir12}
\by A.~B.~Zheglov, A.~E.~Mironov
\paper Baker~-- Akhiezer modules, Krichever sheaves, and commuting rings of partial differential operators
\jour Dal'nevost. Mat. Zh.
\yr 2012
\vol 12
\issue 1
\pages 20--34
\mathnet{http://mi.mathnet.ru/dvmg226}


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    This publication is cited in the following articles:
    1. A. B. Zheglov, “On rings of commuting partial differential operators”, St. Petersburg Math. J., 25:5 (2014), 775–814  mathnet  crossref  mathscinet  zmath  isi  elib
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