Annals of Global Analysis and Geometry

, Volume 1, Issue 2, pp 21–90 | Cite as

Arithmetic curves on ball quotient surfaces

  • Rolf-Peter Holzapfel
Article

Keywords

Intersection Graph Minimal Resolution Chern Number Quotient Singularity Singularity Resolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    BAILY, W.L.,Jr. and BOREL,A.: Compactification of arithmetic quotients of bounded symmetric domains,Ann. Math.84 (1966), 442–528MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    BANICA, C. and STANASILA, O.: Algebraic methods in the global theory of complex spaces, J. Wiley & sons, London, New York, Sydney, Toronto (1976)MATHGoogle Scholar
  3. [3]
    BOREL, A.: Linear algebraic groups, Benjamin, New York, Amsterdam (1969)MATHGoogle Scholar
  4. [4]
    BOREL, A.: Introduction aux groupes arithmétiques, Hermann, Paris (1969)MATHGoogle Scholar
  5. [5]
    BOREL, A.: Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem, J. Diff. Geom.6 (1972), 543–560MathSciNetMATHGoogle Scholar
  6. [6]
    BOURBAKI, N.: Groupes et algèbres de Lie, Hermann, Paris (1968)MATHGoogle Scholar
  7. [7]
    BRIESKORN, E.: Rationale Singularitäten komplexer Flächen, Inv. math..4 (1967), 336–358MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    CHEVALLEY, C.: Invariants of finite groups generated by reflections, Am. Journ. Math.77 (1955), 778–782MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    DIEUDONNE, J.: La Géométrie des groupes classiques, Springer, Berlin, Heidelberg, New York (1971)MATHGoogle Scholar
  10. [10]
    FEUSTEL, J.-M.: Über die Spitzen von Modulflächen zur zweidimensionalen komplexen Einheitskugel, Preprintreihe des ZIMM, AdW d.DDR, Berlin (1977)Google Scholar
  11. [11]
    FEUSTEL, J.-M.: Spiegelungs- and Spitzenkontributionen zum arithmetischen Geschlecht Picardscher Modulflächen, Dissertation, ZIMM, AdW d. DDR, Berlin (1980)Google Scholar
  12. [12]
    Feustel, J.-M. and HOLZAPFEL, R.-P.:. Symmetry points and Chern numbers of Picard modular surfaces, in preparation for Math. Nachr.Google Scholar
  13. [13]
    FUJIKI, A.: On resolutions of cyclic quotient singularities, Publ. RIMS, Kyoto-Univ.10 (1974), 293–328MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    GOTTSCHLING, E.: Die Uniformisierbarkeit der Fixpunkte eigentlich diskontinuierlicher Gruppen van biholomorphen Abbildungen, Math. Ann.169 (1967), 26–54MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    GROTHENDIECK, A. and DIEUDONNE,J.: Eléments de Géométrie algébrique, Publ. Math. I.H.E.S.,4, 8, 11, 17, 20, 24, 28, 32 (1960-68)Google Scholar
  16. [16]
    HARTSHORNE, R.: Algebraic Geometry, Graduate Texts in Math., Vol. 52, Springer, Berlin, Heidelberg, New York (1977)Google Scholar
  17. [17]
    HIRZEBRUCH, F.: Über vierdimensionale Riemannsche Flächen mehrdeutiger analytiseher Funktionen von zwei komplexen Veränderlichen, Math. Ann.126 (1953), 1–22MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    HIRZEBRUCH, F. and VAN DE VEN, A.: Hilbert modular surfaces and the classification of algebraic surfaces, Inv.math.23 (1974), 1–29MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    HOLZAPFEL, R. -P.: Arithmetische Kugelquotientenflächen I, II, Seminarberichte der Humboldt-Universität14, Berlin (1978)Google Scholar
  20. [20]
    HOLZAPFEL, R.-P.: Arithmetische Kugelquotientenflachen III,IV, Sem.Ber.d.Humb.Univ.20 , Berlin (1979)Google Scholar
  21. [21]
    HOLZAPFEL, R.-P.: Arithmetische Kugelquotientenflachen V,VI, Sem.Ber.d.Humb.Univ.21, Berlin (1979)Google Scholar
  22. [22]
    HOLZAPFEL, R.-P.: A class of minimal surfaces in the unknown region of surface geography, Math. Nachr.98 (1980), 211–232MathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    HOLZAPFEL, R.-P.: Invariants of arithmetic ball quotient surfaces, Math. Nachr.103 (1981), 117–153MathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    HOLZAPFEL, R.-P.: Arithmetic surfaces with great K2, to appear in Proc. of Week of Algebr. Geom., Teubner, Leipzig (1981)Google Scholar
  25. [25]
    MIYAOKA, Y.: On the Chern numbers of surfaces of general type, Inv. math.42 (1977), 225–237MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    MIYAOKA,Y.: On algebraic surfaces with positive index, preprint (1980)Google Scholar
  27. [27]
    MUMFORD,D.: Abelian varieties, Lect. in Tata Inst. of fund. research, Bombay (1968)Google Scholar
  28. [28]
    MUMFORD,D.: Introduction to algebraic geometry, Mim. notes, Harvard Univ. (1967)Google Scholar
  29. [29]
    MUMFORD, D.: Hirzebruch's proportionality theorem in the noncompact case, Inv. math.42 (1977), 239–272MathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    PRILL, D.: Local classification of quotients of complex manifolds by discontineous groups, Duke Math. Journ.34 (1967), 375–386MathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    ŠAFAREVIČ, I.R. et al: Algebraic surfaces, Trudi Mat. Inst. Stekl.75 (1965)Google Scholar
  32. [32]
    SCHWARTZMANN, O.W.: On the factor space of an arithmetic discrete group acting on the complex ball, Dissertation, MGU, Moskau (1974)Google Scholar
  33. [33]
    SHIMURA, G.: On purely transcendental fields of automorphic functions of several variables, Osaka Journ. Math.1, No.1, (1964), 1–14MathSciNetMATHGoogle Scholar
  34. [34]
    SHIMURA,G.: Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten Publ., Princ. Univ. Press (1971)Google Scholar
  35. [35]
    YAU, S.-T.: Calabils conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. U.S.A.74 (1977), 1798–1799MathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    FEUSTEL, J.-M.: Kompaktifizierung and Singularitäten des Faktorraumes einer arithmetischen Gruppe, die in der zweidimensionalen Einheitskugel wirkt, Diplomarbeit, Humb.-Univ. Berlin (1976)Google Scholar

Copyright information

© VEB Deutscher Verlag der Wissenchaften 1983

Authors and Affiliations

  • Rolf-Peter Holzapfel
    • 1
  1. 1.Akademie der Wissenschaften der DDRInstitut für Mathemetik (IMath)Berlin

Personalised recommendations