On rings of commuting partial differential operators

Details On rings of commuting partial differential operators On rings of commuting partial differential operators

2011-06-03

arxiv.org/abs/1106.0765v2

Mathematics

Algebraic Geometry

39 p. This is an extended version with corrested typos and inaccuracies in some definitions and claims; several statements and

Scientific paper

We give a natural generalization of the classification of commutative rings of ordinary differential operators, given in works of Krichever, Mumford, Mulase, and determine commutative rings of operators in two variables (satisfying certain mild conditions) in terms of Parshin's generalized geometric data. It uses a generalization of M.Sato's theory and is constructible in both ways.

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