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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
Commuting differential operators and higher-dimensional algebraic varieties
H. Kurkea, D. Osipovb, A. Zheglovc a Department of Mathematics, Faculty of Mathematics and Natural Sciences II, Humboldt University of
Berlin, Unter den Linden 6, 10099 Berlin, Germany
b Algebra and Number Theory Department, Steklov Mathematical Institute, Gubkina str. 8,
119991 Moscow, Russia
c Department of Differential Geometry and Applications, Faculty of Mechanics and Mathematics,
Lomonosov Moscow State University, Leninskie Gory, GSP,
119899 Moscow, Russia
Аннотация:
Several algebro-geometric properties of commutative rings of partial differential operators (PDOs) as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of PDOs, and we investigate the properties of these geometric data. This construction is in some sense 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 PDOs in two variables. As a by-product, we get several necessary conditions on geometric data describing commutative rings of PDOs.
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