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Baker, Note on the Foregoing Paper “Commutative ordinary differential operators, byJ. L. Burchnall and T. W. Chaundy” , Proceedings Royal Soc. London (A) 118, 584–593(1928).32. Bass H., Algebraic -theory, Benjamin, New York, 196819533. A. Beilinson, V. Drinfeld, Quantization of Hitchin’s system and Hecke eigensheaves,Preprint, available at http://www.math.uchicago.edu/ mitya/langlands/hitchin/BDhitchin.pdf34. Beilinson A. A., Schechtman V. V., Determinant bundles and Virasoro algebra, Comm.Math. Physics, 118 (1988), 651-70135.
Ben-Zvi D., Frenkel E., Spectral curves, opers and integrable systems, Publ. Math., Inst.Hautes Etud. Sci. 94, 87-159 (2001).36. Yu. Berest, A. Kasman D-modules and Darboux transformations, Lett. Math. Phys., vol.43, 3, 1998, 279–29437. Berest Yu., Etingof P., Ginzburg V., Cherednik algebras and differential operators on quasiinvariants, Duke Math. J. 118 (2), 279-337 (2003)38. A. Borel et al., Algebraic D-modules, Perspectives in Mathematics, 2.
Academic Press,(1987).39. Braverman A., Etingof P., Gaitsgory D., Quantum integrable systems and differential Galoistheory, Transfor. Groups 2, 31-57 (1997)40. W. Bruns, J. Herzog, Cohen-Macaulay rings. Rev. ed., Cambridge Studies in AdvancedMathematics, 39, Cambridge University Press, Cambridge, 199841. I. Burban, A. Zheglov, Fourier-Mukai transform on Weierstrass cubics and commutingdifferential operators, Oberwolfach preprints, v.3, 2016, 1-32;42. Burban I., Drozd Y., Maximal Cohen-Macaulay modules over non-isolated surfacesingularities and matrix problems, to appear in the Memoirs of the AMS; arXiv:1002.304243. Burban I., Drozd Y., Maximal Cohen-Macaulay modules over surface singularities, Trendsin representation theory of algebras and related topics, 101-166, EMS Ser.
Congr. Rep.,Eur. Math. Soc., Zürich, 2008.44. Burchnall J.L., Chaundy T.W., Commutative ordinary differential operators, Proc. LondonMath. Soc. Ser. 2, 21 (1923) 420-440; Proc. Royal Soc. London Ser. A, 118 (1928) 557-583.45. J. Burchnall, T. Chaundy, Commutative ordinary differential operators, Proc. RoyalSoc. London (A) 118, 557–583 (1928).46. J. Burchnall, T.
Chaundy, Commutative ordinary differential operators. II: The identity = , Proc. Royal Soc. London (A) 134, 471–485 (1931).47. Chalykh O., Algebro-geometric Schrödinger operators in many dimensions, Philos. Trans.R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 366, No. 1867, 947-971 (2008).48. Chalykh O., Veselov A., Commutative rings of partial differential operators and Lie algebras,Comm.
Math. Phys. 125 (1990) 597-611.49. Chalykh O., Veselov A., Integrability in the theory of the Schrödinger operators andharmonic analysis, Comm. Math. Phys. 152 (1993) 29-40.50. Chalykh O., Styrkas K., Veselov A., Algebraic integrability for the Schrödinger operatorsand reflections groups, Theor. Math. Phys. 94 (1993) 253-275.19651. E. Date, M. Jimbo, M. Kashiwara and T. Miwa, Transformation groups for solitonequations, in M.
Jimbo and T. Miwa, Non-linear integrable systems – Classical theoryand quantum theory, Word Scientific, 289 pps, 198352. V.N. Davletshina, On self-adjoint commuting differential operators of rank two, SiberianElectronic Math. Reports 10 (2013), 109–112.53. V.N.
Davletshina, Commuting differential operators of rank two with trighonometriccoefficients, Siberian Math. J., 56:3 (2015), 405-410.54. V.N. Davletshina, E.I. Shamaev, On commuting differential operators of rank 2, SiberianMath. J., 55:4 (2014), 606–610.55. J. Dixmier, Sur les algèbres de Weyl, Bull. Soc. Math. France 96 (1968) 209–242.56. P.
Dehornoy, Opérateurs différentiels et courbes elliptiques, Comp. Math. 43 (1981), 71–99.57. Drinfeld V., Infinite Infinite-dimensional vector bundles in algebraic geometry: anintroduction. The unity of mathematics. In honor of the ninetieth birthday of I.
M. Gelfand.Papers from the conference held in Cambridge, MA, USA, August 31–September 4, 2003.Boston, MA: Birkhauser. Progress in Mathematics 244, 263-304 (2006).58. Dubrovin B., Theta functions and non-linear equations, Russ. Math. Surv. 36, No.2, 11-92(1981).59. Dubrovin B. A., Krichever I. M., Novikov S. P., Integrable systems I, in: Dynamical systemsIV, eds. V.I.Arnold, S.P.Novikov (Springer, Berlin, 1990) pp. 173-280.60.
Grothendieck A., Sur quelques points d’algebre homologique, Tohoku Math. J., 9 (1957),119-221.61. Grothendieck A., Technique de descente et théorèms d’existence en géométrie algébrique.V. Les schémas de Picard: théorèmes d’existence, Seminaire Bourbaki, Vol. 7, Exp. No.232, 142-161, Soc. Math.
France, Paris, 1995.62. Grothendieck A., Dieudonné J.A., Eléments de géométrie algébrique I, Springer, 1971.63. Grothendieck A., Dieudonné J.A., Éléments de géométrie algébrique II, Publ. Math.I.H.E.S., 8 (1961).64. Grothendieck A., Dieudonné J.A., Éléments de géométrie algébrique III, Publ. Math.I.H.E.S., 11 (1961).65. Grothendieck A., Dieudonné J.A., Éléments de géométrie algébrique IV, Publ. Math.I.H.E.S., 20 (1964).66.
P. Etingof, Lectures on Calogero-Moser systems, arXiv:math/060623367. Etingof P., Ginzburg V., On m-quasi-invariants of a Coxeter group, Mosc. Math. J. 2(3),555-566 (2002)68. Faltings G., Über Macaulayfizierung, Math.Ann. 238, 175-192 (1978).69. Feigin M., Veselov A.P., Quasi-invariants of Coxeter groups and m-harmonic polynomials,IMRN 2002 (10), 2487-2511 (2002)19770. Feigin M., Veselov A.P., Quasi-invariants and quantum integrals of deformed CalogeroMoser systems, IMRN 2003 (46), 2487-2511 (2003)71.
Ferrand D., Conducteur, descente et pincement, Bull. Soc. math. France, 131 (4), 2003,p.553-585.72. Fulton W. Intersection theory, Springer, Berlin-Heilderberg-New York 1998.73. F. Grünbaum, Commuting pairs of linear ordinary differential operators of orders four andsix, Phys. D 31 (1988), 424–433.74. R. Hirota, Direct methods of finding exact solutions of nonlinear evolution equations, inLect. Notes in Math.
515, Springer-Verlag, 197675. D. Huybrechts, M. Lehn, The geometry of moduli spaces of sheaves. 2nd ed., Cambridge,Cambridge University Press, 201076. A. Ya. Kanel-Belov, M. L. Kontsevich, The Jacobian conjecture is stably equivalent to theDixmier conjecture, Mosc. Math. J., 7:2 (2007), 209—218.77. Kapranov M., The elliptic curve in the -duality theory and Eisenstein series for KacMoody groups.
e-print arXiv:math/0001005.78. Kapranov M., Vasserot E., Vertex algebras and the formal loop space, Publ. Math. IHES,100 (2004), 209-269.79. Kashiwara M., The flag manifold of Kac-Moody Lie algebra, in Algebraic analysis, geometryand number theory, Johns Hopkins University Press, Baltimore, 1989, 161-19080.
A. Kasman, E. Previato, Commutative partial differential operators, Physica D., 152–153,2001, 66–7781. S. Kleiman, Towards a numerical theory of ampleness, Annals of Math. 84, 1966, 293-344.82. H. Kojima, T. Takahashi, Notes on the minimal compactifications of the affine plane, Annalidi Matematica Pura ed Applicata, 188, 1, 2010, 153–169.83.
M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airyfunction, Comm. Math. Phys. 147, 1992, 1-2384. Kurke H., Osipov D., Zheglov A., Formal punctured ribbons and two-dimensional local fields,Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2009, Issue629, Pages 133 - 170;85. Kurke H., Osipov D., Zheglov A., Formal groups arising from formal punctured ribbons,Int. J.
of Math., 06 (2010), 755-797.86. H. Kurke, D. Osipov, A. Zheglov, Commuting differential operators and higher–dimensionalalgebraic varieties, Selecta Math. 20 (2014), 1159–1195.87. Lax P.D.:Integrals of nonlinear equations of evolution and solitary waves, Commun. PureAppl.
Math. 21, (1968), 467-49088. Lazarsfeld R., Positivity in algebraic geometry I, Ergebnisse der Mathematik, vol. 48,Springer-Verlag, Heidelberg, 2004.19889. Lipman J., Picard schemes of formal schemes; Application to rings with discrete divisorclass group, in Classification of algebraic varieties and compact complex manifolds (LNM412, Springer-Verlag, Berlin-Heidelberg-New York, 1974), pp. 94-132.90. Manin Y., Algebraic aspects of nonlinear differential equations, Itogi Nauki Tekh., Ser.Sovrem. Probl. Mat. 11, 5-152 (1978).91. Matsumura H., Commutative algebra, W.A. Benjamin Co., New York, 1970.92.
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