Commuting families in skew fields and quantization of Beauville's fibration
Enriquez, Benjamin ; Rubtsov, Vladimir
Duke Math. J., Tome 120 (2003) no. 3, p. 197-219 / Harvested from Project Euclid
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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 A. 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.
Publié le : 2003-08-15
Classification:  53D50,  12E15,  14Hxx,  14Jxx 
@article{1082744731,
     author = {Enriquez, Benjamin and Rubtsov, Vladimir},
     title = {Commuting families in skew fields and quantization of Beauville's fibration},
     journal = {Duke Math. J.},
     volume = {120},
     number = {3},
     year = {2003},
     pages = { 197-219},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082744731}
}

Enriquez, Benjamin; Rubtsov, Vladimir. Commuting families in skew fields and quantization of Beauville's fibration. Duke Math. J., Tome 120 (2003) no. 3, pp.  197-219. http://gdmltest.u-ga.fr/item/1082744731/