Skip to main content
SpringerLink
Log in

Finite groups of automorphisms of K3 surfaces and the Mathieur group

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Atiyah, M.F., Segal, G.B.: The index of elliptic operators: II. Ann. Math.87, 531–545 (1968)

    Google Scholar 

  2. Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. (Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 4). Berlin-Heidelberg-New York: Springer 1984

    Google Scholar 

  3. Blichfeldt, H.F.: Finite collineation groups. The Univ. of Chicago Press 1917

  4. Brauer, R.: Simple group of order 5·2a·3b (Collected works, Vol. II, pp. 421–470). Boston, MA: MIT Press 1980

    Google Scholar 

  5. Burnside, W.: Theory of groups of finite order, 2nd ed. Cambridge University Press 1911

  6. Conway, J.H.: Three lectures on exceptional groups. (Finite simple groups, pp. 215–247). New York: Academic Press 1971

    Google Scholar 

  7. Frobenius, G.: Über die Charaktere der mehrfach transitiven Gruppen. Sitzungsber. Akad. Wiss. DDR, Math.-Naturwiss. Kl. pp. 558–571 (1904)

  8. Gaschütz, W.: Zur Erweiterungstheorie der endlichen Gruppen. J. Reine Angew. Math.190, 93–107 (1952)

    Google Scholar 

  9. Hall, M., Senior, J.K.: The groups of order 2n (n≦6). New York: McMillan 1964

    Google Scholar 

  10. Huppert, B.: Endlichen Gruppen I. (Die Grundhlehren der Mathematischen Wissenschaften in Einzeldarstellungen, Band 134). Berlin-Heidelberg-New York: Springer 1967

    Google Scholar 

  11. Klein, F.: Vorlesungen über Ikosaeder. Leipzig: Teubner 1884

    Google Scholar 

  12. Kneser, M.: Über die Ausnahme-Isomorphismen zwischen endlichen klassischen Gruppen. Abh. Math. Semin. Univ. Hamb.31, 136–140 (1967)

    Google Scholar 

  13. Kodaira, K.: On the structure of compact complex analytic surfaces, I. Am. J. Math.86, 751–798 (1984)

    Google Scholar 

  14. Maschke, H.: Über die quaternäre, endliche, lineare Substitutionsgruppe der Borchardt'schen Moduln. Math. Ann.30, 496–515 (1887)

    Google Scholar 

  15. Maschke, H.: Aufstellung des vollen Formensystems einer quarternären Gruppe von 51840 linearen Substitutionen. Math. Ann.33, 317–344 (1889)

    Google Scholar 

  16. Mathieu, É. L.: Mémoire sur l'étude des fonctions de plusieurs quantités sur la manière de les former et sur les substitutions qui les laissent invariables. J. Math. Pure Appl.6, 241–323 (1861)

    Google Scholar 

  17. Mathieu, É. L.: Sur la fonction cinq fois transitive de 24 quantités. J. Math. Pure Appl.18, 25–46 (1873)

    Google Scholar 

  18. Morrison, D.: Letter dated on 18th of July in 1983

  19. Nikulin, V.V.: Finite groups of automorphisms of Kählerian surfaces of type K3 (English translation). Moscow Math. Soc.38, 71–137 (1980)

    Google Scholar 

  20. Witt, E.: Die 5-fach transitiven Gruppen von Mathieu. Hamburg Abh.12, 256–264 (1938)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Nagoya University, Furó-chó Chikusa-ku, Nagoya 464, Japan

    Shigeru Mukai

Authors
  1. Shigeru Mukai
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mukai, S. Finite groups of automorphisms of K3 surfaces and the Mathieur group. Invent Math 94, 183–221 (1988). https://doi.org/10.1007/BF01394352

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01394352

Keywords

Search

Navigation