Keywords
- Modulus Space
- Vector Bundle
- Line Bundle
- Unitary Representation
- Betti Number
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Bibliography
M.F. Atiyah: Vector bundles over an elliptic curve. Proc. London Math. Soc. 7 (1957), 414–452.
M.F. Atiyah and R. Bott: The Yang-Mills equations on a Riemann surface. Phil. Trans. Royal Soc. Lond. A 308 (1982), 523–621.
U.V. Desale and S. Ramanan: Classification of vector bundles of rank 2 on hyper-elliptic curves, Inventiones Math., 38 (1976), 161–185.
G. Harder: Eine Bemurkung zu einer Arbeit von P.E. Newstead. Jour. für. Math. 242 (1970), 16–25.
G. Harder and M.S. Narasimhan: On the cohomology groups of moduli spaces of vector bundles on curves, Math. Annalen 212 (1975), 215–248.
D. Mumford: Geometric Invariant Theory, Springer Verlag, 1965.
D. Mumford: Projective invariants of projective structures and applications, Proc. International Congress of Math., (Stockholm 1962), 526–530.
D. Mumford and P.E. Newstead: Periods of a moduli space of bundles on curves. Amer. J. Math. 90 (1968), 1200–1208.
M.S. Narasimhan: Vector bundles on compact Riemann surfaces, in Complex Analysis and its Applications, Vol. III, International Atomic Energy Agency, Vienna, 1976.
M.S. Narasimhan and S. Ramanan: Vector bundles on curves, in Algebraic Geometry, Bombay Colloquium 1968, (O.U.P. 1969), 335–346.
M.S. Narasimhan and S. Ramanan: Moduli of vector bundles on a compact Riemann surface, Ann. of Math. 89 (1969), 14–51.
M.S. Narasimhan and S. Ramanan: Deformations of the moduli space of vector bundles on an algebraic curve, Ann. of Math. 101 (1975), 391–417.
M.S. Narasimhan and S. Ramanan: Generalized prym varieties as fixed points, J. Indian Math. Soc. 39 (1975), 1–19.
M.S. Narasimhan and S. Ramanan: Geometry of Hecke Cycles I, In C.P. Ramanujan-A Tribute (T.I.F.R. Studies in Math.) Springer-Verlag, 1978, 291–345.
M.S. Narasimhan and C.S. Seshadri: Holomorphic vector bundles on a compact Riemann surface, Math. Annalen 155 (1964), 69–80.
M.S. Narasimhan and C.S. Seshadri: Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. 82 (1965), 540–567.
P.E. Newstead: Introduction to moduli problems and orbit spaces, T.I.F.R. Lecture Notes, Springer-Verlag, 1978.
P.E. Newstead: Topological properties of some spaces of stable bundles, Topology 6 (1967), 241–262.
P.E. Newstead: Stable bundles of rank 2 and odd degree over a curve of genus 2, Topology 7 (1968), 205–215.
P.E. Newstead: Characteristic classes of stable bundles of rank 2 over an algebraic curve, Trans. Amer. Math. Soc. 169 (1972), 337–345.
P.E. Newstead: Rationality of moduli spaces of stable bundles, Math. Annalen 215 (1975), 251–268, Correction in 249 (1980) 281.
S. Ramanan: The moduli spaces of vector bundles over an algebraic curve, Math. Annalen 200 (1973), 69–84.
C.S. Seshadri: Space of unitary vector bundles on a compact Riemann surface, Ann. of Math. 85 (1967), 303–336.
C.S. Seshadri: Desingularisation of the moduli variety of vector bundles on curves, Proc. Int. Symp. Alg. Geom. Kyoto 1977, Kinokuniya, Tokyo, 1978.
C.S. Seshadri: Fibrés vectoriels sur les courbes algébriques (rédigé par J.M. Drezet), Astérisque (96), 1982.
A. Tjurin: Analogue of Torelli’s theorem for two dimensional bundles over algebraic curves of arbitrary genus Izv. Akad. Nauk. SSSR. Ser. Mat. 30 (1966), 1353–1356, English trans., Math. U.S.S.R. Izv 3 (1969), 1081–1101.
A. Tjurin: Analogues of Torelli’s theorem for multidimensional vector bundles over an arbitrary algebraic curve, Izv. Akad. Nauk, SSSR Ser Mat. 34 (1970), 338–365, English trans., Math. U.S.S.R.-Izv 4 (1970), 343–370.
A. Tjurin: The geometry of moduli of vector bundles, Uspehi Mat. Nauk 29: 6 (1974) 59–88, English trans., Russian Math. Surveys 29: 6 (1974), 57–88.
J.-L. Verdier and J. Le Potier (Editors): Module des fibrés stables sur les courbes algébriques, Progress in Maths. vol. 54, Birkhäuser, 1985.
A. Weil: Généralisation des functions abéliennes, J. Math. Pures Appl. 17 (1938), 47–87.
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© 1987 Springer-Verlag
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Narasimhan, M.S. (1987). Survey of vector bundles on curves. In: Greuel, GM., Trautmann, G. (eds) Singularities, Representation of Algebras, and Vector Bundles. Lecture Notes in Mathematics, vol 1273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078835
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DOI: https://doi.org/10.1007/BFb0078835
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