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On rings of commuting partial differential operators

Research paper by A. B. Zheglov

Indexed on: 12 Dec '12Published on: 12 Dec '12Published in: Mathematics - Algebraic Geometry



Abstract

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 a completed ring of partial differential 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.