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Volumn 148, Issue 1, 1998, Pages 109-196

Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface

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EID: 0032347790     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/120993     Document Type: Article
Times cited : (81)

References (52)
  • 1
    • 84874962985 scopus 로고
    • Convexity and commuting Hamiltonians
    • M. F. ATIYAH, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15.
    • (1982) Bull. London Math. Soc. , vol.14 , pp. 1-15
    • Atiyah, M.F.1
  • 2
    • 0000979746 scopus 로고
    • The Yang-Mills equations over Riemann surfaces
    • M. F. ATIYAH and R. BOTT, The Yang-Mills equations over Riemann surfaces. Phil. Trans. Roy. Soc. Lond. A308 (1983), 523-615.
    • (1983) Phil. Trans. Roy. Soc. Lond. , vol.A308 , pp. 523-615
    • Atiyah, M.F.1    Bott, R.2
  • 3
    • 0009781709 scopus 로고
    • The moment map and equivariant cohomology
    • _, The moment map and equivariant cohomology, Topology 23 (1984), 1-28.
    • (1984) Topology , vol.23 , pp. 1-28
  • 4
    • 52249110413 scopus 로고
    • Geometric quantization of Chern-Simons gauge theory
    • S. AXELROD, S. DELLA PIETRA, and E. WITTEN, Geometric quantization of Chern-Simons gauge theory, J. Diff. Geom. 33 (1991), 787-902.
    • (1991) J. Diff. Geom. , vol.33 , pp. 787-902
    • Axelrod, S.1    Della Pietra, S.2    Witten, E.3
  • 5
    • 0040011144 scopus 로고
    • Vector bundles on curves and generalized theta functions: Recent results and open problems, preprint alg-geom/9404001
    • Cambridge Univ. Press
    • A. BEAUVILLE, Vector bundles on curves and generalized theta functions: recent results and open problems, preprint alg-geom/9404001 (1994) Math. Sci. Res. Inst. Publ. 28, Cambridge Univ. Press, 1995.
    • (1994) Math. Sci. Res. Inst. Publ. , vol.28
    • Beauville, A.1
  • 6
    • 21844499806 scopus 로고
    • Conformal blocks and generalized theta functions
    • A. BEAUVILLE and Y. LASZLO, Conformal blocks and generalized theta functions, Commun. Math. Phys. 164 (1994), 385-519.
    • (1994) Commun. Math. Phys. , vol.164 , pp. 385-519
    • Beauville, A.1    Laszlo, Y.2
  • 8
    • 0000334608 scopus 로고
    • Classes caractéristiques équivariantes. Formules de localisation en cohomologie équivariante
    • N. BERLINE et M. VERGNE, Classes caractéristiques équivariantes. Formules de localisation en cohomologie équivariante, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), 539-541.
    • (1982) C. R. Acad. Sci. Paris Sér. I Math , vol.295 , pp. 539-541
    • Berline, N.1    Vergne, M.2
  • 9
    • 84972570445 scopus 로고
    • Zéros d'un champ de vecteurs et classes caractéristiques équivariantes
    • _, Zéros d'un champ de vecteurs et classes caractéristiques équivariantes, Duke Math. J. 50 (1983), 539-549.
    • (1983) Duke Math. J. , vol.50 , pp. 539-549
  • 10
    • 0001878907 scopus 로고
    • On the de Rham theory of certain classifying spaces
    • R. BOTT, H. SHULMAN, and J. STASHEFF, On the de Rham theory of certain classifying spaces, Adv. Math. 20 (1976), 43-50.
    • (1976) Adv. Math. , vol.20 , pp. 43-50
    • Bott, R.1    Shulman, H.2    Stasheff, J.3
  • 13
    • 0000275289 scopus 로고
    • Poincaré polynomials of the variety of stable bundles
    • U. V. DESALE and S. RAMANAN, Poincaré polynomials of the variety of stable bundles, Math. Ann. 216 (1975), 233-244.
    • (1975) Math. Ann. , vol.216 , pp. 233-244
    • Desale, U.V.1    Ramanan, S.2
  • 15
    • 0002731705 scopus 로고
    • Gluing techniques in the cohomology of moduli spaces
    • (Proc. 1991 conf., Stony Brook, NY in honour of the sixtieth birthday of J. Milnor), Publish or Perish
    • S. K. DONALDSON, Gluing techniques in the cohomology of moduli spaces, in Topological Methods in Modern Mathematics (Proc. 1991 conf., Stony Brook, NY in honour of the sixtieth birthday of J. Milnor), Publish or Perish, 1993, 137-170.
    • (1993) Topological Methods in Modern Mathematics , pp. 137-170
    • Donaldson, S.K.1
  • 16
    • 0041197157 scopus 로고
    • Groupe de picard des variétés de modules de fibrés semi-stables sur les courbes algébriques
    • J.-M. DREZET et M. S. NARASIMHAN, Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent. Math. 97 (1989), 53-94.
    • (1989) Invent. Math. , vol.97 , pp. 53-94
    • Drezet, J.-M.1    Narasimhan, M.S.2
  • 17
    • 34250229086 scopus 로고
    • On the variation in the cohomology of the symplectic form of the reduced phase space
    • Addendum, 72 (1983), 153-158
    • J. J DUISTERMAAT and G. HECKMAN, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982), 259-268; Addendum, 72 (1983), 153-158.
    • (1982) Invent. Math. , vol.69 , pp. 259-268
    • Duistermaat, J.J.1    Heckman, G.2
  • 18
    • 0042837866 scopus 로고
    • Equivariant cohomology and stationary phase
    • Utrecht preprint (Sanda and Yokohama, 1993)
    • J. J. DUISTERMAAT, Equivariant cohomology and stationary phase, Utrecht preprint no. 817 (1993): in Symplectic Geometry and Quantization (Sanda and Yokohama, 1993), Y. Maeda, H. Omori and A. Weinstein, eds.; Contemp. Math., Amer. Math. Soc. 179 (1994), 45-62.
    • (1993) Symplectic Geometry and Quantization , vol.817
    • Duistermaat, J.J.1
  • 19
    • 0040011143 scopus 로고
    • J. J. DUISTERMAAT, Equivariant cohomology and stationary phase, Utrecht preprint no. 817 (1993): in Symplectic Geometry and Quantization (Sanda and Yokohama, 1993), Y. Maeda, H. Omori and A. Weinstein, eds.; Contemp. Math., Amer. Math. Soc. 179 (1994), 45-62.
    • (1994) Contemp. Math., Amer. Math. Soc. , vol.179 , pp. 45-62
    • Maeda, Y.1    Omori, H.2    Weinstein, A.3
  • 20
    • 0001834722 scopus 로고
    • Orbites coadjointes et cohomologie équivariante
    • M. Duflo, N. V. Pedersen, M. Vergue (eds.), Progress in Mathematics, Birkhauser
    • M. DUFLO et M. VERGNE, Orbites coadjointes et cohomologie équivariante, in M. Duflo, N. V. Pedersen, M. Vergue (eds.), The Orbit Method in Representation Theory (Progress in Mathematics, vol. 82), Birkhauser, (1990) 11-60.
    • (1990) The Orbit Method in Representation Theory , vol.82 , pp. 11-60
    • Duflo, M.1    Vergne, M.2
  • 21
    • 0000405473 scopus 로고
    • A proof for the Verlinde formula
    • G. FALTINGS, A proof for the Verlinde formula, J. Alg. Geom. 3 (1994), 347-374.
    • (1994) J. Alg. Geom. , vol.3 , pp. 347-374
    • Faltings, G.1
  • 22
    • 34247181532 scopus 로고
    • String theory on group manifolds
    • D. GEPNER and K. WITTEN, String theory on group manifolds, Nucl. Phys. B 278 (1986), 493-549.
    • (1986) Nucl. Phys. B , vol.278 , pp. 493-549
    • Gepner, D.1    Witten, K.2
  • 24
    • 84979027600 scopus 로고    scopus 로고
    • The Jeffrey-Kirwan localization theorem and residue operations in equivariant cohomology
    • V. GUILLEMIN and J. KALKMAN, The Jeffrey-Kirwan localization theorem and residue operations in equivariant cohomology, J. Reine Angew. Math. 470 (1996), 123-142.
    • (1996) J. Reine Angew. Math. , vol.470 , pp. 123-142
    • Guillemin, V.1    Kalkman, J.2
  • 25
    • 0000567544 scopus 로고
    • Convexity properties of the moment mapping
    • V. GUILLEMIN and S. STERNBERG, Convexity properties of the moment mapping, Invent. Math. 67 (1982), 491-513.
    • (1982) Invent. Math. , vol.67 , pp. 491-513
    • Guillemin, V.1    Sternberg, S.2
  • 26
    • 34250418355 scopus 로고
    • On the cohomology groups of moduli spaces of vector bundles over curves
    • G. HARPER, and M. S. NARASIMHAN, On the cohomology groups of moduli spaces of vector bundles over curves, Math. Ann. 212 (1975), 215-248.
    • (1975) Math. Ann. , vol.212 , pp. 215-248
    • Harper, G.1    Narasimhan, M.S.2
  • 29
    • 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. Annalen 298 (1994), 667-692.
    • (1994) Math. Annalen , vol.298 , pp. 667-692
    • Jeffrey, L.C.1
  • 30
    • 0009155755 scopus 로고    scopus 로고
    • Symplectic forms on moduli spaces of flat connections on 2-manifolds
    • Athens, GA, 1993, ed. W. Kazez. AMS
    • _, Symplectic forms on moduli spaces of flat connections on 2-manifolds, in Proc. Georgia Intern. Topology Conf. (Athens, GA, 1993), ed. W. Kazez. AMS (1997) 268-281.
    • (1997) Proc. Georgia Intern. Topology Conf. , pp. 268-281
  • 31
    • 84974002329 scopus 로고
    • Group cohomology construction of the cohomology of moduli spaces of flat connections on 2-manifolds
    • _, Group cohomology construction of the cohomology of moduli spaces of flat connections on 2-manifolds, Duke Math. J. 77 (1995), 407-429.
    • (1995) Duke Math. J. , vol.77 , pp. 407-429
  • 32
    • 0344544526 scopus 로고
    • Localization for nonabelian group actions
    • L. C. JEFFREY and F. C. KIRWAN, Localization for nonabelian group actions, Topology 34 (1995), 291-327.
    • (1995) Topology , vol.34 , pp. 291-327
    • Jeffrey, L.C.1    Kirwan, F.C.2
  • 33
    • 0001854036 scopus 로고
    • Intersection pairings in moduli spaces of holomorphic bundles on a Riemann surface
    • _, Intersection pairings in moduli spaces of holomorphic bundles on a Riemann surface. Elec. Res. Announ. AMS 1 (1995), 57-71.
    • (1995) Elec. Res. Announ. AMS , vol.1 , pp. 57-71
  • 34
    • 0031138789 scopus 로고    scopus 로고
    • Localization and the quantization conjecture
    • _, Localization and the quantization conjecture, Topology 36 (1997), 647-693.
    • (1997) Topology , vol.36 , pp. 647-693
  • 35
    • 21144468299 scopus 로고
    • BRST model for equivariant cohomology and representatives for the equivariant Thom class
    • J. KALKMAN, BRST model for equivariant cohomology and representatives for the equivariant Thom class, Commun. Math. Phys. 153 (1993), 447-463.
    • (1993) Commun. Math. Phys. , vol.153 , pp. 447-463
    • Kalkman, J.1
  • 36
    • 0002201305 scopus 로고
    • Cohomology rings of symplectic quotients
    • _, Cohomology rings of symplectic quotients, J. Reine Angew. Math. 458 (1995), 37-52.
    • (1995) J. Reine Angew. Math. , vol.458 , pp. 37-52
  • 37
    • 0003312306 scopus 로고
    • Cohomology of quotients in symplectic and algebraic geometry
    • Princeton University Press
    • F. KIRWAN, Cohomology of Quotients in Symplectic and Algebraic Geometry, Math. Notes 31 Princeton University Press (1984).
    • (1984) Math. Notes , vol.31
    • Kirwan, F.1
  • 38
    • 84968519541 scopus 로고
    • The cohomology rings of moduli spaces of bundles over Riemann surfaces
    • _, The cohomology rings of moduli spaces of bundles over Riemann surfaces. J. A. M. S. 5 (1992), 853-906.
    • (1992) J. A. M. S. , vol.5 , pp. 853-906
  • 39
    • 0002082888 scopus 로고
    • Infinite Grassmannians and moduli spaces of G-bundles
    • S. KUMAR, M. S. NARASIMHAN, and A. RAMANATHAN, Infinite Grassmannians and moduli spaces of G-bundles, Math. Ann. 300 (1994), 41-75.
    • (1994) Math. Ann. , vol.300 , pp. 41-75
    • Kumar, S.1    Narasimhan, M.S.2    Ramanathan, A.3
  • 41
    • 0000055829 scopus 로고
    • Superconnections, Thom classes, and equivariant differential forms
    • V. MATHAI and D. QUILLEN, Superconnections, Thom classes, and equivariant differential forms, Topology 25 (1986), 85-110.
    • (1986) Topology , vol.25 , pp. 85-110
    • Mathai, V.1    Quillen, D.2
  • 42
    • 0001690431 scopus 로고
    • Stable and unitary vector bundles on a compact Riemann surface
    • M. S. NARASIMHAN and C. S. SESHADRI, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. 82 (1965), 540-567.
    • (1965) Ann. of Math. , vol.82 , pp. 540-567
    • Narasimhan, M.S.1    Seshadri, C.S.2
  • 43
    • 0001686899 scopus 로고
    • Characteristic classes of stable bundles of rank 2 over an algebraic curve
    • P. NEWSTEAD, Characteristic classes of stable bundles of rank 2 over an algebraic curve, Trans. Amer. Math. Soc. 169 (1972), 337-345.
    • (1972) Trans. Amer. Math. Soc. , vol.169 , pp. 337-345
    • Newstead, P.1
  • 44
    • 11244319351 scopus 로고
    • Determinants of Cauchy-Riemann operators over a Riemann surface
    • D. G. QUILLEN, Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl. 19 (1985), 31-34.
    • (1985) Funct. Anal. Appl. , vol.19 , pp. 31-34
    • Quillen, D.G.1
  • 46
    • 0002589236 scopus 로고
    • The combinatorics of the Verlinde formulas, alg-geom/9402003
    • ed. N. Hitchin LMS Lecture Note Series A. Szenes, private communication
    • A. SZENES, The combinatorics of the Verlinde formulas, alg-geom/9402003 in Vector Bundles in Algebraic Geometry, ed. N. Hitchin (LMS Lecture Note Series 208), 1995; A. Szenes, private communication.
    • (1995) Vector Bundles in Algebraic Geometry , vol.208
    • Szenes, A.1
  • 48
    • 84972535630 scopus 로고
    • Conformal field theory and the cohomology of the moduli space of stable bundles
    • M. THADDEUS, Conformal field theory and the cohomology of the moduli space of stable bundles, J. Diff. Geom. 35 (1992), 131-149.
    • (1992) J. Diff. Geom. , vol.35 , pp. 131-149
    • Thaddeus, M.1
  • 49
    • 0000333180 scopus 로고
    • Conformal field theory on universal family of stable curves with gauge symmetries
    • Academic Press
    • A. TSUCHIYA, K. UENO, and Y. YAMADA, Conformal field theory on universal family of stable curves with gauge symmetries, Advanced Studies in Pure Math. 19, Academic Press (1989), 459-566.
    • (1989) Advanced Studies in Pure Math. , vol.19 , pp. 459-566
    • Tsuchiya, A.1    Ueno, K.2    Yamada, Y.3
  • 50
    • 0242310336 scopus 로고
    • On quantum gauge theories in two dimensions
    • E. WITTEN, On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991), 153-209.
    • (1991) Comm. Math. Phys. , vol.141 , pp. 153-209
    • Witten, E.1
  • 51
    • 17144427930 scopus 로고
    • Two dimensional gauge theories revisited
    • preprint hep-th/9204083
    • _, Two dimensional gauge theories revisited, preprint hep-th/9204083: J. Geom. Phys. 9 (1992), 303-368.
    • (1992) J. Geom. Phys. , vol.9 , pp. 303-368
  • 52
    • 0000992313 scopus 로고
    • An integration formula for the square of moment maps of circle actions
    • preprint hep-th/9212071
    • S. WU, An integration formula for the square of moment maps of circle actions, preprint hep-th/9212071: Lett. Math. Phys. 29 (1993), 311-328.
    • (1993) Lett. Math. Phys. , vol.29 , pp. 311-328
    • Wu, S.1


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