The line bundles on the moduli of parabolic G-bundles over curves and their sections
Laszlo, Yves ; Sorger, Christoph
Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997), p. 499-525 / Harvested from Numdam
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@article{ASENS_1997_4_30_4_499_0,
     author = {Laszlo, Yves and Sorger, Christoph},
     title = {The line bundles on the moduli of parabolic $G$-bundles over curves and their sections},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {30},
     year = {1997},
     pages = {499-525},
     doi = {10.1016/s0012-9593(97)89929-6},
     mrnumber = {98f:14007},
     zbl = {0918.14004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1997_4_30_4_499_0}
}

Laszlo, Yves; Sorger, Christoph. The line bundles on the moduli of parabolic $G$-bundles over curves and their sections. Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997) pp. 499-525. doi : 10.1016/s0012-9593(97)89929-6. http://gdmltest.u-ga.fr/item/ASENS_1997_4_30_4_499_0/

[1] A. Beauville, Conformal blocks, fusion rules and the Verlinde formula, Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry, (Israel Math. Conf. Proc., Vol. 9, 1996). | MR 97f:17025 | Zbl 0848.17024

[2] A. Beauville, Fibrés de rang deux sur une courbe, fibré déterminant et fonctions thêta, II, (Bull. Soc. math. France, Vol. 119, 1991, pp. 259-291). | Numdam | MR 92m:14041 | Zbl 0756.14017

[3] A. Beauville and Y. Laszlo, Conformal blocks and generalized theta functions, (Comm. Math. Physics, Vol. 164, 1994, pp. 385-419). | MR 95k:14011 | Zbl 0815.14015

[4] A. Beauville and Y. Laszlo, A result on algebraic descent, (Comptes Rendus Acad. Sci. Paris, Vol. 320, Série I, 1995, pp. 335-340). | MR 96a:14049 | Zbl 0852.13005

[5] R. Bott, Homogeneous vector bundles, (Ann. of Math., Series 2, Vol. 66, 1957, pp. 203-248). | MR 19,681d | Zbl 0094.35701

[6] E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, (AMS Transl. Ser. II, Vol. 6, 1957, pp. 111-244). | Zbl 0077.03404

[7] J.-M. Drezet and M. S. Narasimhan, Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, (Inv. math., Vol. 97, 1989, pp. 53-94). | MR 90d:14008 | Zbl 0689.14012

[8] V. Drinfeld and C. Simpson, B-structures on G-bundles and local triviality, (Math.-Res.-Lett., Vol. 2, 1995, pp. 823-829). | MR 96k:14013 | Zbl 0874.14043

[9] G. Faltings, Stable G-bundles and projective connections, (J. Alg. Geometry, Vol. 2, 1993, pp. 507-568). | MR 94i:14015 | Zbl 0790.14019

[10] G. Faltings, A proof of the Verlinde formula, (J. Alg. Geometry, Vol. 3, 1994, pp. 347-374). | MR 95j:14013 | Zbl 0809.14009

[11] R. Fossum and B. Iversen, On Picard groups of algebraic fiber spaces, (J. pure and appl. algebra, Vol. 3, 1973, pp. 269-280). | MR 50 #9864 | Zbl 0277.14005

[12] V.G. Kac, Infinite dimensional Lie algebras (Third edition), Cambride, (Cambridge University Press, 1990). | MR 92k:17038 | Zbl 0716.17022

[13] G. Kempf, Deformations of Semi-Euler Characteristics, (Amer. J. of Math., Vol. 114, 1992, pp. 973-978). | MR 93k:14025 | Zbl 0780.14012

[14] F. Knudsen and D. Mumford, The projectivity of the moduli space of stable curves I : preliminaries on “det” and “div”, (Math. Scand., Vol. 39, 1976, pp. 19-55). | MR 55 #10465 | Zbl 0343.14008

[15] S. Kumar, Demazure character formula in arbitrary Kac-Moody setting, (Inv. math., Vol. 89, 1987, pp. 395-423). | MR 88i:17018 | Zbl 0635.14023

[16] S. Kumar, M. S. Narasimhan and A. Ramanathan, Infinite Grassmannians and Moduli Spaces of G-bundles, (Math. Annalen, Vol. 300, 1994, pp. 395-423). | MR 96e:14011 | Zbl 0803.14012

[17] S. Kumar and M. S. Narasimhan, Picard group of the moduli spaces of G-bundles (e-print alg-geom/9511012). | Zbl 0884.14004

[18] G. Laumon and L. Moret-Bailly, Champs algébriques, (Preprint Université Paris 11 (Orsay), 1992).

[19] G. Laumon and M. Rapoport, The Langlands lemma and the Betti numbers of stacks of G-bundles on a curve, (Internat. J. Math., Vol. 7, 1996, pp. 29-45). | MR 97f:14012 | Zbl 0871.14028

[20] O. Mathieu, Formules de caractères pour les algèbres de Kac-Moody générales, (Astérisque, Vol. 159-160, 1988). | MR 90d:17024 | Zbl 0683.17010

[21] V. B. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, (Math. Annales, Vol. 248, 1980, pp. 205-239). | MR 81i:14010 | Zbl 0454.14006

[22] D. Mumford, Theta characteristics on an algebraic curve, (Ann. Sci. École Norm. Sup., Vol. 4, 1971, pp. 181-192). | Numdam | MR 45 #1918 | Zbl 0216.05904

[23] C. Pauly, Espaces de modules paraboliques et blocks conformes, (Duke Math. J., Vol. 84, 1996, pp. 217-235). | MR 97h:14022 | Zbl 0877.14031

[24] A. Ramanathan, Stable Principal G-bundles, PhD. Thesis, (Bombay University, 1976).

[25] I. R. Shafarevich, On some infinite-dimensional groups, (II Math. USSR-Izv., Vol. 18, 1982, pp. 185-194). | Zbl 0491.14025

[26] P. Slodowy, On the geometry of Schubert varieties attached to Kac-Moody Lie algebras, (Can. Math. Soc. Conf Proc., Vol. 6, 1984, pp. 405-442). | MR 87i:14043 | Zbl 0591.14038

[27] Ch. Sorger, Thêta-caractéristiques des courbes tracées sur une surface lisse, (J. reine angew. Math., Vol. 435, 1993, pp. 83-118). | MR 94b:14026 | Zbl 0757.14024

[28] Ch. Sorger, La semi-caractéristique d'Euler-Poincaré des faisceaux ⍵-quadratiques sur un schéma de Cohen-Macaulay, (Bull. Soc. Math. France, Vol. 122, 1994, pp. 225-233). | Numdam | Zbl 0814.14020

[29] Ch. Sorger, La formule de Verlinde, (Séminaire Bourbaki, No 794, 1994). | Numdam | Zbl 0878.17024

[30] R. Steinberg, Générateurs, relations et revêtements de groupes algébriques, (Colloque sur la théorie des groupes algébriques, Bruxelles, Gauthier-Villars, Paris, 1962, pp. 113-127). | MR 27 #3638 | Zbl 0272.20036

[31] A. Tsuchiya, K. Ueno and Y. Yamada, Conformal Field Theory on Universal Family of Stable Curves with Gauge Symmetries, (Adv. Studies in Pure Math., Vol. 19, 1989, pp. 459-566). | MR 92a:81191 | Zbl 0696.17010