Geodesic
Baker~-- Akhiezer modules, Krichever sheaves, and commuting rings of partial differential operators
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 20-34

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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. 
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     author = {A. B. Zheglov and A. E. Mironov},
     title = {Baker~-- {Akhiezer} modules, {Krichever} sheaves, and commuting rings of partial differential operators},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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A. B. Zheglov; A. E. Mironov. Baker~-- Akhiezer modules, Krichever sheaves, and commuting rings of partial differential operators. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 20-34. http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a2/