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

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.

### MSC:

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

Zbl 0827.58022
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### References:

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