Duke Mathematical Journal

Niemeier lattices, Mathieu groups, and finite groups of symplectic automorphisms of K3 surfaces

Shigeyuki Kondō

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Article information

Source
Duke Math. J., Volume 92, Number 3 (1998), 593-603.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077231678

Digital Object Identifier
doi:10.1215/S0012-7094-98-09217-1

Mathematical Reviews number (MathSciNet)
MR1620514

Zentralblatt MATH identifier
0958.14025

Subjects
Primary: 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 11H06: Lattices and convex bodies [See also 11P21, 52C05, 52C07] 14J50: Automorphisms of surfaces and higher-dimensional varieties

Citation

Kondō, Shigeyuki. Niemeier lattices, Mathieu groups, and finite groups of symplectic automorphisms of $K3$ surfaces. Duke Math. J. 92 (1998), no. 3, 593--603. doi:10.1215/S0012-7094-98-09217-1. https://projecteuclid.org/euclid.dmj/1077231678


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References

  • [1] J. H. Conway, Three lectures on exceptional groups, Finite simple groups (Proc. Instructional Conf., Oxford, 1969), Academic Press, London, 1971, pp. 215–247.
  • [2] S. Kondō, Niemeier lattices, Mathieu groups, and finite groups of symplectic automorphisms of $K3$ surfaces, Duke Math. J. 92 (1998), no. 3, 593–603.
  • [3] S. Mukai, Finite groups of automorphisms of $K3$ surfaces and the Mathieu group, Invent. Math. 94 (1988), no. 1, 183–221.
  • [4] V. V. Nikulin, Finite groups of automorphisms of Kählerian $K3$ surfaces, Trudy Moskov. Mat. Obshch. 38 (1979), 75–137.
  • [5] V. V. Nikulin, Integer symmetric bilinear forms and some of their geometric applications, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 1, 111–177, 238.
  • [6] T. Shioda and H. Inose, On singular $K3$ surfaces, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo, 1977, pp. 119–136.
  • [7] G. Xiao, Galois covers between $K3$ surfaces, Ann. Inst. Fourier (Grenoble) 46 (1996), no. 1, 73–88.