Commuting families in skew fields and quantization of Beauville's fibration

Details Commuting families in skew fields and quantization of Beauville's fibration Commuting families in skew fields and quantization of Beauville's fibration

2001-12-26

arxiv.org/abs/math/0112276v1

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

Mathematics

Algebraic Geometry

Scientific paper

We construct commuting families in fraction fields of symmetric powers 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 fibrations introduced by Beauville. When S is the canonical cone of an algebraic curve C, we construct commuting families of differential operators on symmetric powers of C, quantizing the Beauville systems.

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