Geodesic
Baker–Akhiezer Modules on Rational Varieties
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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The free Baker–Akhiezer modules on rational varieties obtained from $\mathbb CP^1\times\mathbb CP^{n-1}$ by identification of two hypersurfaces are constructed. The corollary of this construction is the existence of embedding of meromorphic function ring with some fixed pole into the ring of matrix differential operators in $n$ variables.
Keywords: commuting differential operators; Baker–Akhiezer modules. 
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     author = {Irina A. Melnik and Andrey E. Mironov},
     title = {Baker{\textendash}Akhiezer {Modules} on {Rational} {Varieties}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a29/}
}
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Irina A. Melnik; Andrey E. Mironov. Baker–Akhiezer Modules on Rational Varieties. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a29/

[1] Nakayashiki A., “Structure of Baker–Akhiezer modules of principally polarized Abelian varieties, commuting partial differential operators and associated integrable systems”, Duke Math. J., 62 (1991), 315–358 | DOI | MR | Zbl

[2] Nakayashiki A., “Commuting partial differential operators and vector bundles over Abelian varieties”, Amer. J. Math., 116 (1994), 65–100 | DOI | MR | Zbl

[3] Mironov A. E., “Commutative rings of differential operators corresponding to multidimensional algebraic varieties”, Siberian Math. J., 43 (2002), 888–898, arXiv: math-ph/0211006 | DOI | MR | Zbl

[4] Rothstein M., “Sheaves with connection on Abelian varieties”, Duke Math. J., 84 (1996), 565–598, arXiv: alg-geom/9602023 | DOI | MR | Zbl

[5] Rothstein M., “Dynamics of the Krichever construction in several variables”, J. Reine Angew. Math., 572 (2004), 111–138, arXiv: math.AG/0201066 | DOI | MR | Zbl

[6] Previato E., “Multivariable Burchnall–Chaundy theory”, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 336 (2008), 1155–1177 | DOI | MR