Commuting differential operators and higher-dimensional algebraic varieties

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.

25 p V2: minor change V3: revised version, to appear in Selecta Math V4: an inaccuracy in Th.2.1 is fixed

References in corpus (3)

• Two dimensional KP systems and their solvability
• Quasi-invariants and quantum integrals of the deformed Calogero--Moser systems
• Commutative Rings of Differential Operators Corresponding to Multidimensional Algebraic Varieties

Cited by in corpus (7)

• Fourier-Mukai transform on Weierstrass cubics and commuting differential operators
• Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems
• Geometric properties of commutative subalgebras of partial differential operators
• Schur-Sato theory for quasi-elliptic rings
• On rings of commuting partial differential operators
• A class of Baker-Akhiezer arrangements
• Normal forms for ordinary differential operators, III