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Izv. Akad. Nauk SSSR Ser. Mat., 1965, Volume 29, Issue 3, Pages 657–688 (Mi izv2927)  

This article is cited in 29 scientific papers (total in 30 papers)

The classification of vector bundles over an algebraic curve of arbitrary genus

A. N. Tyurin


Full text: PDF file (2767 kB)

English version:
Amer. Math. Soc. Transl. Ser. 2, 1967, 63, 245–279

Bibliographic databases:
UDC: 513.6
Received: 10.08.1964

Citation: A. N. Tyurin, “The classification of vector bundles over an algebraic curve of arbitrary genus”, Izv. Akad. Nauk SSSR Ser. Mat., 29:3 (1965), 657–688; Amer. Math. Soc. Transl. Ser. 2, 63 (1967), 245–279

Citation in format AMSBIB
\Bibitem{Tyu65}
\by A.~N.~Tyurin
\paper The classification of vector bundles over an algebraic curve of arbitrary genus
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1965
\vol 29
\issue 3
\pages 657--688
\mathnet{http://mi.mathnet.ru/izv2927}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=217071}
\zmath{https://zbmath.org/?q=an:0207.51603}
\transl
\jour Amer. Math. Soc. Transl. Ser. 2
\yr 1967
\vol 63
\pages 245--279


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    Erratum

    This publication is cited in the following articles:
    1. A. N. Tyurin, “Analog of Torelli's theorem for two-dimensional bundles over algebraic curves of arbitrary genus”, Math. USSR-Izv., 3:5 (1969), 1081–1101  mathnet  crossref  mathscinet  zmath
    2. A. N. Tyurin, “The geometry of moduli of vector bundles”, Russian Math. Surveys, 29:6 (1974), 57–88  mathnet  crossref  mathscinet  zmath
    3. A. N. Tyurin, “The geometry of the Poincaré theta-divisor of a Prym variety”, Math. USSR-Izv., 9:5 (1975), 951–986  mathnet  crossref  mathscinet  zmath
    4. F. A. Bogomolov, “Holomorphic tensors and vector bundles on projective varieties”, Math. USSR-Izv., 13:3 (1979), 499–555  mathnet  crossref  mathscinet  zmath  isi
    5. I. M. Krichever, “Commutative rings of ordinary linear differential operators”, Funct. Anal. Appl., 12:3 (1978), 175–185  mathnet  crossref  mathscinet  zmath
    6. I. M. Krichever, S. P. Novikov, “Holomorphic bundles over Riemann surfaces and the Kadomtsev–Petviashvili equation. I”, Funct. Anal. Appl., 12:4 (1978), 276–286  mathnet  crossref  mathscinet  zmath
    7. I. M. Krichever, S. P. Novikov, “Holomorphic bundles over algebraic curves and non-linear equations”, Russian Math. Surveys, 35:6 (1980), 53–79  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. I. M. Krichever, “Baxter's equations and algebraic geometry”, Funct. Anal. Appl., 15:2 (1981), 92–103  mathnet  crossref  mathscinet  zmath  isi
    9. O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Math. USSR-Izv., 35:3 (1990), 629–655  mathnet  crossref  mathscinet  zmath
    10. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. N. Tyurin, “Algebraic geometric aspects of smooth structure. I. The Donaldson polynomials”, Russian Math. Surveys, 44:3 (1989), 113–178  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. O. K. Sheinman, “Krichever–Novikov algebras and self-duality equations on Riemann surfaces”, Russian Math. Surveys, 56:1 (2001), 176–178  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. O. K. Sheinman, “The Fermion Model of Representations of Affine Krichever–Novikov Algebras”, Funct. Anal. Appl., 35:3 (2001), 209–219  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. O. K. Sheinman, “Second order Casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$”, Mosc. Math. J., 1:4 (2001), 605–628  mathnet  mathscinet  zmath
    15. I. M. Krichever, “Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations”, Mosc. Math. J., 2:4 (2002), 717–752  mathnet  mathscinet  zmath  elib
    16. I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    18. O. K. Sheinman, “Krichever–Novikov Algebras, their Representations and Applications in Geometry and Mathematical Physics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S85–S161  mathnet  crossref  crossref  zmath
    19. I. M. Krichever, O. K. Sheinman, “Lax Operator Algebras”, Funct. Anal. Appl., 41:4 (2007), 284–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. M. Schlichenmaier, O. K. Sheinman, “Central extensions of Lax operator algebras”, Russian Math. Surveys, 63:4 (2008), 727–766  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    21. O. K. Sheinman, “Lax Operator Algebras and Integrable Hierarchies”, Proc. Steklov Inst. Math., 263 (2008), 204–213  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    22. O. K. Sheinman, “Lax operator algebras and Hamiltonian integrable hierarchies”, Russian Math. Surveys, 66:1 (2011), 145–171  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. D. V. Artamonov, “The Number of Additional Singular Points in the Riemann–Hilbert Problem on a Riemann Surface”, Math. Notes, 90:1 (2011), 3–9  mathnet  crossref  crossref  mathscinet  zmath  isi
    24. M. Schlichenmaier, “Multipoint Lax operator algebras: almost-graded structure and central extensions”, Sb. Math., 205:5 (2014), 722–762  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. O. K. Sheinman, “Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface”, Proc. Steklov Inst. Math., 290:1 (2015), 178–188  mathnet  crossref  crossref  isi  elib  elib
    26. O. K. Sheinman, “Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras”, Theoret. and Math. Phys., 185:3 (2015), 1816–1831  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    27. Oleg K. Sheinman, “Global current algebras and localization on Riemann surfaces”, Mosc. Math. J., 15:4 (2015), 833–846  mathnet  mathscinet  zmath  elib
    28. O. K. Sheinman, “Lax operator algebras and integrable systems”, Russian Math. Surveys, 71:1 (2016), 109–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. O. K. Sheinman, “Matrix divisors on Riemann surfaces and Lax operator algebras”, Trans. Moscow Math. Soc., 78 (2017), 109–121  mathnet  crossref  elib
    30. E. V. Semenko, “Reduction of vector boundary value problems on Riemann surfaces to one-dimensional problems”, Siberian Math. J., 60:1 (2019), 153–163  mathnet  crossref  crossref  isi
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