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Volumn 53, Issue 3, 2003, Pages

Parabolic bundles, products of conjugacy classes and Gromov-Witten invariants

Author keywords

Gromov Witten invariants; Moment polytopes; Parabolic bundles; Quantum cohomology

Indexed keywords


EID: 0346328167     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1957     Document Type: Article
Times cited : (45)

References (54)
  • 1
    • 0032216971 scopus 로고    scopus 로고
    • Eigenvalues of products of unitary matrices and quantum Schubert calculus
    • S. AGNIHOTRI and C. WOODWARD, Eigenvalues of products of unitary matrices and quantum Schubert calculus, Math. Res. Lett., 5-6 (1998), 817-836.
    • (1998) Math. Res. Lett. , vol.5-6 , pp. 817-836
    • Agnihotri, S.1    Woodward, C.2
  • 4
    • 0035629766 scopus 로고    scopus 로고
    • Principal bundles over projective manifolds with parabolic structure over a divisor
    • V. BALAJI, I. BISWAS and D. S. NAGARAJ, Principal bundles over projective manifolds with parabolic structure over a divisor, Tohoku Math. J. (2), 53-3 (2001), 337-367.
    • (2001) Tohoku Math. J. (2) , vol.53 , Issue.3 , pp. 337-367
    • Balaji, V.1    Biswas, I.2    Nagaraj, D.S.3
  • 6
    • 0345843240 scopus 로고    scopus 로고
    • The Picard group of the moduli of G-bundles on a curve
    • to appear
    • A. BEAUVILLE, Y. LASZLO and Ch. SORGER, The Picard group of the moduli of G-bundles on a curve, Compositio Math., to appear.
    • Compositio Math.
    • Beauville, A.1    Laszlo, Y.2    Sorger, Ch.3
  • 7
    • 0042787774 scopus 로고    scopus 로고
    • 1 - S for S a finite set
    • 1 - S for S a finite set, Compositio Math., 129-1 (2001), 67-86.
    • (2001) Compositio Math. , vol.129 , Issue.1 , pp. 67-86
    • Belkale, P.1
  • 8
    • 0034379457 scopus 로고    scopus 로고
    • Coadjoint orbits, moment polytopes and the Hilbert-Mumford criterion
    • electronic
    • A. BERENSTEIN and R. SJAMAAR, Coadjoint orbits, moment polytopes and the Hilbert-Mumford criterion, J. Amer. Math. Soc., 13-2 (2000), 433-466 (electronic).
    • (2000) J. Amer. Math. Soc. , vol.13 , Issue.2 , pp. 433-466
    • Berenstein, A.1    Sjamaar, R.2
  • 9
    • 0001256344 scopus 로고
    • Moduli of parabolic G-bundles on curves
    • U. BHOSLE and A. RAMANATHAN, Moduli of parabolic G-bundles on curves, Math. Z., 202-2 (1989), 161-180.
    • (1989) Math. Z. , vol.202 , Issue.2 , pp. 161-180
    • Bhosle, U.1    Ramanathan, A.2
  • 10
    • 0000900140 scopus 로고    scopus 로고
    • Parabolic bundles as orbifold bundles
    • I. BISWAS, Parabolic bundles as orbifold bundles, Duke Math. J., 88-2 (1997), 305-325.
    • (1997) Duke Math. J. , vol.88 , Issue.2 , pp. 305-325
    • Biswas, I.1
  • 11
    • 22044441377 scopus 로고    scopus 로고
    • A criterion for the existence of a parabolic stable bundle of rank two over the projective line
    • I. BISWAS, A criterion for the existence of a parabolic stable bundle of rank two over the projective line, Internat. J. Math., 9-5 (1998), 523-533.
    • (1998) Internat. J. Math. , vol.9 , Issue.5 , pp. 523-533
    • Biswas, I.1
  • 12
    • 51249178893 scopus 로고
    • Representations of orbifold groups and parabolic bundles
    • H. BODEN, Representations of orbifold groups and parabolic bundles, Comment. Math. Helvetici, 66 (1991), 389-447.
    • (1991) Comment. Math. Helvetici , vol.66 , pp. 389-447
    • Boden, H.1
  • 13
    • 0001168858 scopus 로고
    • The topology of the space of stable bundles on a compact Riemann surface
    • G. D. DASKALOPOULOS, The topology of the space of stable bundles on a compact Riemann surface, J. Differential Geom., 36-3 (1992), 699-746.
    • (1992) J. Differential Geom. , vol.36 , Issue.3 , pp. 699-746
    • Daskalopoulos, G.D.1
  • 14
    • 0034412892 scopus 로고    scopus 로고
    • The Yang-Mills flow near the boundary of Teichmüller space
    • G. D. DASKALOPOULOS and R. A. WENTWORTH, The Yang-Mills flow near the boundary of Teichmüller space, Math. Ann., 318-1 (2000), 1-42.
    • (2000) Math. Ann. , vol.318 , Issue.1 , pp. 1-42
    • Daskalopoulos, G.D.1    Wentworth, R.A.2
  • 15
    • 0002661058 scopus 로고    scopus 로고
    • Variation of geometric invariant theory quotients
    • with an appendix by Nicolas Ressayre
    • I. V. DOLGACHEV and Y. Hu, Variation of geometric invariant theory quotients, Inst. Hautes Études Sci. Publ. Math., 87 (1998), 5-56, with an appendix by Nicolas Ressayre.
    • (1998) Inst. Hautes Études Sci. Publ. Math. , vol.87 , pp. 5-56
    • Dolgachev, I.V.1    Hu, Y.2
  • 17
    • 21844502353 scopus 로고
    • B-structures on G-bundles and local triviality
    • V. G. DRINFELD and C. SIMPSON, B-structures on G-bundles and local triviality, Math. Res. Lett., 2-6 (1995), 823-829.
    • (1995) Math. Res. Lett. , vol.2-6 , pp. 823-829
    • Drinfeld, V.G.1    Simpson, C.2
  • 18
  • 19
    • 0035600381 scopus 로고    scopus 로고
    • K-area, Hofer metric and geometry of conjugacy classes in Lie groups
    • M. ENTOV, K-area, Hofer metric and geometry of conjugacy classes in Lie groups, Invent. Math., 146-1 (2001), 93-141.
    • (2001) Invent. Math. , vol.146 , Issue.1 , pp. 93-141
    • Entov, M.1
  • 20
    • 0000342893 scopus 로고
    • Stable G-bundles and projective connections
    • G. FALTINGS, Stable G-bundles and projective connections, J. Algebraic Geom., 2-3 (1993), 507-568.
    • (1993) J. Algebraic Geom. , vol.2-3 , pp. 507-568
    • Faltings, G.1
  • 21
    • 0001842831 scopus 로고    scopus 로고
    • Notes on stable maps and quantum cohomology
    • Amer. Math. Soc., Providence, RI
    • W. FULTON and R. PANDHARIPANDE, Notes on stable maps and quantum cohomology.In Algebraic geometry-Santa Cruz 1995, pages 45-96. Amer. Math. Soc., Providence, RI, 1997.
    • (1997) Algebraic Geometry-Santa Cruz 1995 , pp. 45-96
    • Fulton, W.1    Pandharipande, R.2
  • 23
    • 44049112686 scopus 로고
    • Seifert fibred homology 3-spheres and the Yang-Mills equations on Riemann surfaces with marked points
    • M. FURUTA and B. STEER, Seifert fibred homology 3-spheres and the Yang-Mills equations on Riemann surfaces with marked points, Adv. Math., 96-1 (1992), 38-102.
    • (1992) Adv. Math. , vol.96 , Issue.1 , pp. 38-102
    • Furuta, M.1    Steer, B.2
  • 24
    • 84972537209 scopus 로고
    • A theorem on compact semi-simple groups
    • M. GOTÔ, A theorem on compact semi-simple groups, J. Math. Soc. Japan, 1 (1949), 270-272.
    • (1949) J. Math. Soc. Japan , vol.1 , pp. 270-272
    • Gotô, M.1
  • 25
    • 0000455623 scopus 로고
    • Sur la classification des fibrés holomorphes sur la sphére de Riemann
    • A. GROTHENDIECK, Sur la classification des fibrés holomorphes sur la sphére de Riemann, Amer. J. Math., 79 (1957), 121-138.
    • (1957) Amer. J. Math. , vol.79 , pp. 121-138
    • Grothendieck, A.1
  • 26
    • 0003274751 scopus 로고
    • Éléments de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphismes
    • A. GROTHENDIECK, Éléments de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphismes, Inst. Hautes Études Sci. Publ. Math., 8 (1961), 222.
    • (1961) Inst. Hautes Études Sci. Publ. Math. , vol.8 , pp. 222
    • Grothendieck, A.1
  • 27
    • 0009976844 scopus 로고
    • Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. I
    • A. GROTHENDIECK, Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. I, Inst. Hautes Études Sci. Publ. Math., 11 (1961), 167.
    • (1961) Inst. Hautes Études Sci. Publ. Math. , vol.11 , pp. 167
    • Grothendieck, A.1
  • 28
    • 0003322387 scopus 로고
    • Algebraic Geometry
    • Springer-Verlag, Berlin-Heidelberg-New York
    • R. HARTSHORNE, Algebraic Geometry, volume 52 of Graduate Texts in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
    • (1977) Graduate Texts in Mathematic , vol.52
    • Hartshorne, R.1
  • 29
    • 0001256234 scopus 로고
    • An equivariant version of Grauert's Oka principle
    • P. HEINZNER and F. KUTZSCHEBAUCH, An equivariant version of Grauert's Oka principle, Invent. Math., 119-2 (1995), 317-346.
    • (1995) Invent. Math. , vol.119 , Issue.2 , pp. 317-346
    • Heinzner, P.1    Kutzschebauch, F.2
  • 30
    • 0002851575 scopus 로고
    • Stable pairs on curves and surfaces
    • D. HUYBRECHTS and M. LEHN, Stable pairs on curves and surfaces, J. Algebraic Geom., 4-1 (1995), 67-104.
    • (1995) J. Algebraic Geom. , vol.4 , Issue.1 , pp. 67-104
    • Huybrechts, D.1    Lehn, M.2
  • 31
    • 0001558153 scopus 로고
    • Extended moduli spaces of flat connections on Riemann surfaces
    • L. C. JEFFREY, Extended moduli spaces of flat connections on Riemann surfaces, Math. Ann., 298 (1994), 667-692.
    • (1994) Math. Ann. , vol.298 , pp. 667-692
    • Jeffrey, L.C.1
  • 32
    • 54649083948 scopus 로고    scopus 로고
    • Stable bundles, representation theory and Hermitian operators
    • A. A. KLYACHKO, Stable bundles, representation theory and Hermitian operators, Selecta Math. (N.S.), 4-3 (1998), 419-445.
    • (1998) Selecta Math. (N.S.) , vol.4 , Issue.3 , pp. 419-445
    • Klyachko, A.A.1
  • 33
    • 0033423661 scopus 로고    scopus 로고
    • n(c) tensor products. I. Proof of the saturation conjecture
    • n(c) tensor products. I. Proof of the saturation conjecture, J. Amer. Math. Soc., 12-4 (1999), 1055-1090.
    • (1999) J. Amer. Math. Soc. , vol.12 , Issue.4 , pp. 1055-1090
    • Knutson, A.1    Tao, T.2
  • 35
    • 0031537223 scopus 로고    scopus 로고
    • The line bundles on the moduli of parabolic G-bundles over curves and their sections
    • Y. LASZLO and C. SORGER, The line bundles on the moduli of parabolic G-bundles over curves and their sections, Ann. Sci. École Norm. Sup. (4), 30-4 (1997), 499-525.
    • (1997) Ann. Sci. École Norm. Sup. (4) , vol.30 , Issue.4 , pp. 499-525
    • Laszlo, Y.1    Sorger, C.2
  • 36
    • 0642332525 scopus 로고
    • Moduli of vector bundles on curves with parabolic structure
    • V.B. MEHTA and C. S. SESHADRI, Moduli of vector bundles on curves with parabolic structure, Math. Ann., 248 (1980), 205-239.
    • (1980) Math. Ann. , vol.248 , pp. 205-239
    • Mehta, V.B.1    Seshadri, C.S.2
  • 37
    • 0001188713 scopus 로고    scopus 로고
    • Hamiltonian loop group actions and Verlinde factorization
    • E. MEINRENKEN and C. WOODWARD, Hamiltonian loop group actions and Verlinde factorization, Journal of Differential Geometry, 50 (1999), 417-470.
    • (1999) Journal of Differential Geometry , vol.50 , pp. 417-470
    • Meinrenken, E.1    Woodward, C.2
  • 39
    • 0039876346 scopus 로고    scopus 로고
    • The red book of varieties and schemes
    • Springer-Verlag, Berlin, expanded edition, Includes the Michigan lectures (1974) on curves and their Jacobians, with contributions by Enrico Arbarello
    • D. MUMFORD, The red book of varieties and schemes, volume 1358 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, expanded edition, 1999, Includes the Michigan lectures (1974) on curves and their Jacobians, with contributions by Enrico Arbarello.
    • (1999) Lecture Notes in Mathematics , vol.1358
    • Mumford, D.1
  • 41
    • 0000209641 scopus 로고    scopus 로고
    • Espaces de modules de fibrés paraboliques et blocs conformes
    • C. PAULY, Espaces de modules de fibrés paraboliques et blocs conformes, Duke Math. J., 84 (1996), 217-235.
    • (1996) Duke Math. J. , vol.84 , pp. 217-235
    • Pauly, C.1
  • 43
    • 0001046466 scopus 로고
    • On the Yang-Mills heat equation in two and three dimensions
    • J. RÅDE, On the Yang-Mills heat equation in two and three dimensions, J. reine angew. Math., 431 (1992), 123-163.
    • (1992) J. Reine Angew. Math. , vol.431 , pp. 123-163
    • Råde, J.1
  • 44
    • 0000742674 scopus 로고    scopus 로고
    • Moduli for principal bundles over algebraic curves, I
    • A. RAMANATHAN, Moduli for principal bundles over algebraic curves, I, Proc. Indian Acad. Sci. Math. Sci., 106-3 (1996), 301-328.
    • (1996) Proc. Indian Acad. Sci. Math. Sci. , vol.106 , Issue.3 , pp. 301-328
    • Ramanathan, A.1
  • 45
    • 0010239127 scopus 로고    scopus 로고
    • Moduli for principal bundles over algebraic curves, II
    • A. RAMANATHAN, Moduli for principal bundles over algebraic curves, II, Proc. Indian Acad. Sci. Math. Sci., 106-4 (1996), 421-449.
    • (1996) Proc. Indian Acad. Sci. Math. Sci. , vol.106 , Issue.4 , pp. 421-449
    • Ramanathan, A.1
  • 47
    • 0003322504 scopus 로고
    • Fibrés vectoriels sur les courbes algébriques
    • Paris. Notes written by J.M. Drezet from a course at the École Normale Supérieure, June 1980
    • C. S. SESHADRI, Fibrés vectoriels sur les courbes algébriques, volume 96 of Astérisque. Société Mathématique de France, Paris, 1982. Notes written by J.M. Drezet from a course at the École Normale Supérieure, June 1980.
    • (1982) Astérisque. Société Mathématique de France , vol.96
    • Seshadri, C.S.1
  • 48
    • 84968515238 scopus 로고
    • Harmonic bundles on noncompact curves
    • C. T. SIMPSON, Harmonic bundles on noncompact curves, J. Amer. Math. Soc., 3-3 (1990), 713-770.
    • (1990) J. Amer. Math. Soc. , vol.3 , Issue.3 , pp. 713-770
    • Simpson, C.T.1
  • 49
    • 0000338256 scopus 로고    scopus 로고
    • Two notes on a finiteness problem in the representation theory of finite groups
    • Algebraic groups and lie groups, Cambridge Univ. Press, Cambridge, with an appendix by G. Martin Cram
    • P. SLODOWY, Two notes on a finiteness problem in the representation theory of finite groups, in Algebraic groups and Lie groups, volume 9 of Austral. Math. Soc. Lect. Ser., pages 331-348, Cambridge Univ. Press, Cambridge, 1997, with an appendix by G. Martin Cram.
    • (1997) Austral. Math. Soc. Lect. Ser. , vol.9 , pp. 331-348
    • Slodowy, P.1
  • 50
    • 0032357238 scopus 로고    scopus 로고
    • Borel-Weil-Bott theory on the moduli stack of G-bundles over a curve
    • C. TELEMAN, Borel-Weil-Bott theory on the moduli stack of G-bundles over a curve, Invent. Math., 134-1 (1998), 1-57.
    • (1998) Invent. Math. , vol.134 , Issue.1 , pp. 1-57
    • Teleman, C.1
  • 51
    • 0034345686 scopus 로고    scopus 로고
    • The quantization conjecture revisited
    • C. TELEMAN, The quantization conjecture revisited, Ann. of Math. (2), 152-1 (2000), 1-43.
    • (2000) Ann. of Math. (2) , vol.152 , Issue.1 , pp. 1-43
    • Teleman, C.1
  • 52
    • 0030531127 scopus 로고    scopus 로고
    • Geometric invariant theory and flips
    • M. THADDEUS, Geometric invariant theory and flips, J. Amer. Math. Soc., 9-3 (1996), 691-723.
    • (1996) J. Amer. Math. Soc. , vol.9 , Issue.3 , pp. 691-723
    • Thaddeus, M.1
  • 53
    • 0000522511 scopus 로고
    • Remarks on the cohomology of groups
    • A. WEIL, Remarks on the cohomology of groups, Ann. of Math. (2), 80 (1964), 149-157.
    • (1964) Ann. of Math. (2) , vol.80 , pp. 149-157
    • Weil, A.1


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