Projective structures and projective bundles over compact Riemann surfaces
Équations différentielles et singularités. En l'honneur de J. M. Aroca, Astérisque, no. 323 (2009), pp. 223-252.
@incollection{AST_2009__323__223_0,
     author = {Loray, Frank and Mar{\'\i}n P\'erez, David},
     title = {Projective structures and projective bundles over compact {Riemann} surfaces},
     booktitle = {\'Equations diff\'erentielles et singularit\'es. En l'honneur de J. M. Aroca},
     editor = {Cano F. and Loray F. and Moralez-Ruiz J. J. and Sad P. and Spivakovsky M.},
     series = {Ast\'erisque},
     pages = {223--252},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {323},
     year = {2009},
     zbl = {1194.30045},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__323__223_0/}
}
TY  - CHAP
AU  - Loray, Frank
AU  - Marín Pérez, David
TI  - Projective structures and projective bundles over compact Riemann surfaces
BT  - Équations différentielles et singularités. En l'honneur de J. M. Aroca
AU  - Collectif
ED  - Cano F.
ED  - Loray F.
ED  - Moralez-Ruiz J. J.
ED  - Sad P.
ED  - Spivakovsky M.
T3  - Astérisque
PY  - 2009
SP  - 223
EP  - 252
IS  - 323
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2009__323__223_0/
LA  - en
ID  - AST_2009__323__223_0
ER  - 
%0 Book Section
%A Loray, Frank
%A Marín Pérez, David
%T Projective structures and projective bundles over compact Riemann surfaces
%B Équations différentielles et singularités. En l'honneur de J. M. Aroca
%A Collectif
%E Cano F.
%E Loray F.
%E Moralez-Ruiz J. J.
%E Sad P.
%E Spivakovsky M.
%S Astérisque
%D 2009
%P 223-252
%N 323
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2009__323__223_0/
%G en
%F AST_2009__323__223_0
Loray, Frank; Marín Pérez, David. Projective structures and projective bundles over compact Riemann surfaces, dans Équations différentielles et singularités. En l'honneur de J. M. Aroca, Astérisque, no. 323 (2009), pp. 223-252. http://www.numdam.org/item/AST_2009__323__223_0/

[1] M. F. Atiyah - "Complex fibre bundles and ruled surfaces", Proc. London Math. Soc. (3) 5 (1955), p. 407-434. | DOI | Zbl

[2] W. Barth, C. Peters & A. Van De Ven - Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 4, Springer, 1984. | Zbl

[3] A. Beilinson & V. Drinfeld - "Opers", preprint arXiv:math/0501398, 2005.

[4] F. Beukers - "Solutions of a Lamé system", private notes, 2004.

[5] G. D. Birkhoff - "A theorem on matrices of analytic functions", Math. Ann. 74 (1913), p. 122-133. | DOI | EuDML | JFM

[6] M. Brunella - Birational geometry of foliations, Monografías de Matemática, Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2000, http://www.impa.br/Publicacoes/Monografias/Abstracts/brunella.ps. | Zbl

[7] C. J. Earle - "On variation of projective structures", in Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N. Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, 1981, p. 87-99. | Zbl

[8] O. Forster - Lectures on Riemann surfaces, Graduate Texts in Mathematics, vol. 81, Springer, 1981. | MR | Zbl

[9] D. Gallo, M. Kapovich & A. Marden - "The monodromy groups of Schwarzian equations on closed Riemann surfaces", Ann. of Math. (2) 151 (2000), p. 625-704. | DOI | EuDML | MR | Zbl

[10] W. M. Goldman - "The symplectic nature of fundamental groups of surfaces", Adv. in Math. 54 (1984), p. 200-225. | DOI | MR | Zbl

[11] X. Gómez-Mont - "Holomorphic foliations in ruled surfaces", Trans. Amer. Math. Soc. 312 (1989), p. 179-201. | DOI | MR | Zbl

[12] R. C. Gunning - "Special coordinate coverings of Riemann surfaces", Math. Ann. 170 (1967), p. 67-86. | DOI | EuDML | MR | Zbl

[13] R. C. Gunning, "Analytic structures on the space of flat vector bundles over a compact Riemann surface", in Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970), Springer, 1971, p. 47-62. Lecture Notes in Math., Vol. 185. | MR | Zbl

[14] R. C. Gunning, "Affine and projective structures on Riemann surfaces", in Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, 1981, p. 225-244. | MR | Zbl

[15] R. Hartshorne - Algebraic geometry, Springer, 1977, Graduate Texts in Mathematics, No. 52. | DOI | MR | Zbl

[16] D. A. Hejhal - "Monodromy groups and linearly polymorphic functions", Acta Math. 135 (1975), p. 1-55. | DOI | MR | Zbl

[17] N. J. Hitchin - "Twistor spaces, Einstein metrics and isomonodromic deformations", J. Differential Geom. 42 (1995), p. 30-112. | DOI | MR | Zbl

[18] J. H. Hubbard - "The monodromy of projective structures", in Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, 1981, p. 257-275. | MR | Zbl

[19] N. M. Katz - "An overview of Deligne's work on Hilbert's twenty-first problem", in Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Vol. XXVIII, Northern Illinois Univ., De Kalb, Ill., 1974), Amer. Math. Soc., 1976, p. 537-557. | MR | Zbl

[20] S. Kawai - "The symplectic nature of the space of projective connections on Riemann surfaces", Math. Ann. 305 (1996), p. 161-182. | DOI | EuDML | MR | Zbl

[21] R. Mandelbaum - "Branched structures on Riemann surfaces", Trans. Amer. Math. Soc. 163 (1972), p. 261-275. | DOI | MR | Zbl

[22] R. Mandelbaum, "Branched structures and affine and projective bundles on Riemann surfaces", Trans. Amer. Math. Soc. 183 (1973), p. 37-58. | DOI | MR | Zbl

[23] R. Mandelbaum, "Unstable bundles and branched structures on Riemann surfaces", Math. Ann. 214 (1975), p. 49-59. | DOI | EuDML | MR | Zbl

[24] M. Maruyama - On classification of ruled surfaces, Lectures in Mathematics, Department of Mathematics, Kyoto University, vol. 3, Kinokuniya Book-Store Co. Ltd., 1970. | MR | Zbl

[25] M. Nagata - "On self-intersection number of a section on a ruled surface", Nagoya Math. J. 37 (1970), p. 191-196. | DOI | MR | Zbl

[26] M. Nagata & M. Maruyama - "Note on the structure of a ruled surface", J. reine angew. Math. 239-240 (1969), p. 68-73. | EuDML | MR | Zbl

[27] M. S. Narasimhan & C. S. Seshadri - "Stable and unitary vector bundles on a compact Riemann surface", Ann. of Math. (2) 82 (1965), p. 540-567. | DOI | MR | Zbl

[28] H. Poincaré - "Sur les groupes des équations linéaires", Acta Math. 4 (1884), p. 201-312. | DOI | JFM | MR

[29] N. Steenrod - The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, 1951. | MR | Zbl

[30] T. Suwa - "On ruled surfaces of genus 1", J. Math. Soc. Japan 21 (1969), p. 291-311. | DOI | MR | Zbl

[31] A. N. Tjurin - "On the classification of two-dimensional fibre bundles over an algebraic curve of arbitrary genus", Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), p. 21-52. | MR

[32] A. N. Tjurin, "Geometry of moduli of vector bundles", Uspehi Mat. Nauk 29 (1974), p. 59-88. | MR | Zbl

[33] A. N. Tjurin, "Periods of quadratic differentials", Uspekhi Mat. Nauk 33 (1978), p. 149-195, 272. | MR | Zbl

[34] A. Weil - "Généralisation des fonctions abéliennes", J. Math. Pures Appl. 17 (1938), p. 47-87. | JFM

[35] A. Weil, "On discrete subgroups of Lie groups", Ann. of Math. (2) 72 (1960), p. 369-384. | DOI | MR | Zbl