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Commutative Rings of Differential Operators Connected with Two-Dimensional Abelian Varieties

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References

  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, No. 2, 315–358 (1991).

    Google Scholar 

  2. Dubrovin B. A., Krichever I. M., and Novikov S. P., “The Schroedinger equation in a periodic magnetic field and Riemann surfaces,” Dokl. Akad. Nauk SSSR, 229, No. 1, 15–19 (1976).

    Google Scholar 

  3. Veselov A. P. and Novikov S. P., “Finite-gap two-dimensional Schr¨odinger operators. Potential operators,” Dokl. Akad. Nauk SSSR, 279, No. 4, 784–788 (1984).

    Google Scholar 

  4. Feldman J., Knorrer H., and Trubowitz E., “There is no two-dimensional analogue of Lame's equation,” Math. Ann., 294, No. 2, 295–324 (1992).

    Google Scholar 

  5. Nakayashiki A., “Commuting partial differential operators and vector bundles over Abelian varieties,” Amer. J. Math., 116, 65–100 (1994).

    Google Scholar 

  6. Mukai S., “Duality between D(X) and D(\(\hat X\)) with its application to Picard sheaves,” Nagoya Math. J., 81, 153–175 (1981).

    Google Scholar 

  7. Andreotti A. and Mayer A., “On period relations for Abelian integrals on algebraic curves,” Ann. Scuola Norm. Sup. Pisa Cl. Sci (4), 21, 189–238 (1967).

    Google Scholar 

  8. Krichever I. M., “The methods of algebraical geometry in the theory of nonlinear equations,” Uspekhi Mat. Nauk, 32, No. 6, 183–208 (1977).

    Google Scholar 

  9. Taimanov I. A., “Secants of Abelian varieties, theta functions, and soliton equations,” Uspekhi Mat. Nauk, 52, No. 1, 149–224 (1997).

    Google Scholar 

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Mironov, A.E. Commutative Rings of Differential Operators Connected with Two-Dimensional Abelian Varieties. Siberian Mathematical Journal 41, 1148–1161 (2000). https://doi.org/10.1023/A:1004832522915

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