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Polynomial periodicity for Betti numbers of covering surfaces

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References

  • [F] Fox, R.H.: Free differential calculus III. Subgroups. Ann. Math.364 (1956)

  • [Gl] Gläser, M.: Arbeitsbericht Sonderforschungsbereich. Bonn. Math. Schr.40 (1983)

  • [G-R] Grauert, H., Remmert, R.: Komplexe Räume. Math. Ann.136 (1958)

  • [Ho] Hironaka, E.: Abelian coverings of the complex projective plane branched along configurations of real lines. In preparation (1990)

  • [Hz] Hirzebruch, F.: Arrangements of lines and algebraic surfaces. In: Artin, M., Task, J. (eds.) Arithmetic Geometry, vol. II. Boston: Birkhäuser 1983

    Google Scholar 

  • [Is] Ishida, M.N.: The irregularities of Hirzebruch's examples of surfaces of general type withc 21 =3c 2. Math. Ann.262, 407–420 (1983)

    Google Scholar 

  • [Iv] Iversen, B.: Numerical invariants and cyclic mutiple planes. Am. J. Math.92, 968–996 (1970)

    Google Scholar 

  • [Lb] Libgober, A.: Alexander polynomial of plane algebraic curves and cyclic multiple planes. Duke Math. J.49(4), 833–851 (1982)

    Google Scholar 

  • [Lf] Laufer H. Normal Two-dimensional Singularities (Ann. Math. Stud.) Princeton, N.J.: Princeton University Press 1971

    Google Scholar 

  • [Lr] Laurent, M.: Equations diophantiennes exponentielles. Invent. Math.78, 299–327 (1984)

    Google Scholar 

  • [M-M] Mayberry, J., Murasugi, K.: Torsion groups of abelian coverings of links. Trans. Am. Math. Soc.271(1), 143–173 (1982)

    Google Scholar 

  • [S] Sarnak, P.: Betti numbers of congruence groups. The Australian National University Research Report. Canberra, Australia (1989)

  • [V] Vacquié, M.: Irregularité des revêtements cycliques des surfaces projective nonsingulieres. (Preprint 1988)

  • [Za1] Zariski, O.: On the linear connection index of algebraic surfaces. Proc. Natl. Acad. Sci. USA, 494–450 (1929)

  • [Za2] Zariski, O.: On the irregularity of cyclic multiple planes. Ann. Math.32, 485–511 (1931)

    Google Scholar 

  • [Zu] Zuo, K.: Kummer-Überlagerungen algebraischer Flächen. Bonn. Math. Schr.193 (1989)

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Authors and Affiliations

  1. Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, W-5300, Bonn 3, Federal Republic of Germany

    Eriko Hironaka

  2. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    Eriko Hironaka

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  1. Eriko Hironaka
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Oblatum 15-II-1991 & 1-VII-1991

Research partially supported by Max-Planck-Institut für Mathematik

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Hironaka, E. Polynomial periodicity for Betti numbers of covering surfaces. Invent Math 108, 289–321 (1992). https://doi.org/10.1007/BF02100607

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