Orbifolds and Their Uniformization

Part of the Progress in Mathematics book series (PM, volume 260)


This is an introduction to complex orbifolds with an emphasis on orbifolds in dimension 2 and covering relations between them.


Orbifold orbiface uniformization ball-quotient 


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  1. [1]
    G. Barthel, F. Hirzebruch, Th. Höfer, Th., Geradenconfigurationen und algebrische Flächen. Aspects of Mathematics D 4, Vieweg, Braunschweig-Wiesbaden, 1986.Google Scholar
  2. [2]
    S. Bundgaard, J. Nielsen, On normal subgroups of finite index in F-groups, Math. Tidsskrift B (1951), 56–58.Google Scholar
  3. [3]
    E.V. Brieskorn, Examples of singular normal complex spaces which are topological manifolds, Proc. Natl. Acad. Sci. USA 55 (1966), 1395–1397.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    H. Cartan, Quotient d’un espace analytique par un groupe d’automorphismes, Algebraic Geometry and Topology, A sympos. in honor of S. Lefschetz, Princeton University Press, 1957, 90–102.Google Scholar
  5. [5]
    C. Chevalley, Invariants of finite groups generated by reflections, Am. J. Math. 77 (1955), 778–782.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    R.H. Fox, On Fenchel’s conjecture about F-groups, Math. Tidsskrift B (1952), 61–65.Google Scholar
  7. [7]
    R.H. Fox, Covering spaces with singularities, Princeton Math. Ser. 12 (1957), 243–257.zbMATHGoogle Scholar
  8. [8]
    E. Hironaka, Abelian coverings of the complex projective plane branched along configurations of real lines, Mem. Am. Math. Soc. 502 (1993).Google Scholar
  9. [9]
    F. Hirzebruch, Arrangements of lines and algebraic surfaces, Progress in Mathematics 36, Birkhäuser, Boston, 1983, 113–140.Google Scholar
  10. [10]
    R.-P. Holzapfel, V. Vladov, Quadric-line configurations degenerating plane Picard-Einstein metrics I–II. Sitzungsber. d. Berliner Math. Ges. 1997–2000, Berlin, 2001, 79–142.Google Scholar
  11. [11]
    B. Hunt, Complex manifold geography in dimension 2 and 3. J. Differ. Geom. 30 no. 1 (1989), 51–153.zbMATHGoogle Scholar
  12. [12]
    J. Kaneko, S. Tokunaga, M. Yoshida, Complex crystallographic groups II, J. Math. Soc. Japan 34 no. 4 (1982), 581–593.MathSciNetCrossRefGoogle Scholar
  13. [13]
    M. Kato, On uniformizations of orbifolds. Adv. Stud. Pure Math. 9 (1987), 149–172.Google Scholar
  14. [14]
    R. Kobayashi, Uniformization of complex surfaces, in: Kähler metric and moduli spaces, Adv. Stud. Pure Math. 18 no. 2 (1990), 313–394.Google Scholar
  15. [15]
    D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Inst. Hautes Études Sci. Publ. Math. 9 (1961), 5–22.zbMATHMathSciNetGoogle Scholar
  16. [16]
    M. Namba, On finite Galois covering germs, Osaka J.Math. 28 no. 1 (1991), 27–35.zbMATHMathSciNetGoogle Scholar
  17. [17]
    M. Namba, Branched coverings and algebraic functions, Pitman Research Notes in Mathematics Series 161, 1987.Google Scholar
  18. [18]
    M. Oka, Some plane curves whose complements have non-abelian fundamental groups, Math. Ann. 218 (1975), 55–65.zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    J.-P. Serre, Revêtements ramifiés du plan projectif Séminaire Bourbaki 204, 1960.Google Scholar
  20. [20]
    G.C. Shephard, J.A. Todd, Finite unitary reflection groups, Can. J. Math. 6 (1954), 274–304.zbMATHMathSciNetGoogle Scholar
  21. [21]
    A.M. Uludağ, Coverings of the plane by K3 surfaces, Kyushu J. Math. 59 no. 2 (2005), 393–419.CrossRefMathSciNetzbMATHGoogle Scholar
  22. [22]
    A.M. Uludağ, Covering relations between ball-quotient orbifolds, Math. An. 308 no. 3 (2004), 503–523.CrossRefGoogle Scholar
  23. [23]
    A.M. Uludağ, On Branched Galois Coverings ofn by products of discs, International J. Math. 4 no. 10 (2003), 1025–1037.Google Scholar
  24. [24]
    A.M. Uludağ, Fundamental groups of a family of rational cuspidal plane curves, Ph.D. thesis, Institut Fourier 2000.Google Scholar
  25. [25]
    M. Yoshida, Fuchsian Differential Equations, Vieweg Aspekte der Math., 1987.Google Scholar
  26. [26]
    O. Zarsiki, On the Purity of the Branch Locus of Algebraic Functions Proc. Natl. Acad. Sci. USA. 44 no. 8 (1958), 791–796.CrossRefGoogle Scholar

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© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Mathematics DepartmentGalatasaray UniversityOrtaköy/IstanbulTurkey

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