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Commuting differential operators and higher-dimensional algebraic varieties

Research paper by Herbert Kurke, Denis Osipov, Alexander Zheglov

Indexed on: 07 Mar '14Published on: 07 Mar '14Published in: Mathematics - Algebraic Geometry



Abstract

Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of partial differential operators, and we investigate the properties of these geometric data. This construction is similar to the construction of a formal module of Baker-Akhieser functions. On the other hand, there is a recent generalization of Sato's theory which belongs to the third author of this paper. We compare both approaches to the commutative rings of partial differential operators in two variables.