Commuting families in skew fields and quantization of Beauville’s fibration. (English) Zbl 1052.53065

Enriquez, Benjamin; Rubtsov, Vladimir

Duke Math. J. 119, No. 2, 197-219 (2003).

From the summary: The authors construct commutating families in fraction fields of symmetric power of algebras. The classical limit of this construction gives Poisson commuting families associated with linear systems. In the case of a \(K3\)-surface \(S\), they correspond to Lagrangian fibration introduced by A. Beauville [Symp. Math. 32, 25–31 (1991; Zbl 0827.58022)]. When \(S\) is the canonical cone of a curve \(C\), the authors construct commutating families of differential operators on symmetric powers of \(C\), quantizing the Beauville systems.

Reviewer: Benjamin Cahen (Metz)

MSC:

53D50	Geometric quantization
14H70	Relationships between algebraic curves and integrable systems
12E15	Skew fields, division rings
14J99	Surfaces and higher-dimensional varieties

Keywords:

commuting families in skew fields; quantization; Beauville’s fibration

Citations:

Zbl 0827.58022

References:

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