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arXiv · 1211.0976

Commuting differential operators and higher-dimensional algebraic varieties

Herbert Kurke·Denis Osipov·Alexander Zheglov
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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.

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Herbert Kurke, Denis Osipov, Alexander Zheglov. 2012-11-05. Commuting differential operators and higher-dimensional algebraic varieties. https://doi.org/10.1007/s00029-014-0155-9

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