Michigan Mathematical Journal

Classification of involutions on Enriques surfaces

Hiroki Ito and Hisanori Ohashi

Full-text: Open access

Article information

Source
Michigan Math. J., Volume 63, Issue 1 (2014), 159-188.

Dates
First available in Project Euclid: 19 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1395234363

Digital Object Identifier
doi:10.1307/mmj/1395234363

Mathematical Reviews number (MathSciNet)
MR3189472

Zentralblatt MATH identifier
1290.14026

Subjects
Primary: 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14J10: Families, moduli, classification: algebraic theory 14J50: Automorphisms of surfaces and higher-dimensional varieties

Citation

Ito, Hiroki; Ohashi, Hisanori. Classification of involutions on Enriques surfaces. Michigan Math. J. 63 (2014), no. 1, 159--188. doi:10.1307/mmj/1395234363. https://projecteuclid.org/euclid.mmj/1395234363


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References

  • W. Barth, K. Hulek, C. Peters, and A. Van de Ven, Compact complex surfaces, Springer-Verlag, Berlin, 2004.
  • W. Barth and C. Peters, Automorphisms of Enriques surfaces, Invent. Math. 73 (1983), 383–411.
  • I. Dolgachev, On automorphisms of Enriques surfaces, Invent. Math. 76 (1984), 163–177.
  • P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1994.
  • E. Horikawa, On the periods of Enriques surfaces. I–II, Math. Ann. 234 (1978), 73–88; 235 (1978), 217–246.
  • K. Hulek and M. Schütt, Enriques surfaces and Jacobian elliptic $K$3 surfaces, Math. Z. 268 (2011), 1025–1056.
  • S. Kondo, Enriques surfaces with finite automorphism groups, Jpn. J. Math. 12 (1986), 191–282.
  • D. R. Morrison, On $K$3 surfaces with large Picard number, Invent. Math. 75 (1984), 105–121.
  • S. Mukai, Numerically trivial involutions of Kummer type of an Enriques surface, Kyoto J. Math. 50 (2010), 889–902.
  • ––––, Kummer's quartics and numerically reflective involutions of Enriques surfaces, J. Math. Soc. Japan 64 (2012), 231–246.
  • S. Mukai and Y. Namikawa, Automorphisms of Enriques surfaces which act trivially on the cohomology groups, Invent. Math. 77 (1984), 383–397.
  • V. V. Nikulin, Finite automorphism groups of Kähler $K$3 surfaces, Trans. Moscow Math. Soc. 38 (1980), 71–135.
  • ––––, Integral symmetric bilinear forms and some of their applications (English translation), Math. USSR Izv. 14 (1980), 103–167.
  • ––––, Factor groups of groups of automorphisms of hyperbolic forms with respect to subgroups generated by 2-reflections, J. Soviet Math. 22 (1983), 1401–1475.
  • ––––, Involutions of integral quadratic forms and their applications to real algebraic geometry, Math. USSR Izv. 22 (1984), 99–172.
  • I. I. Piatetski-Shapiro and I. R. Shafarevich, A Torelli theorem for algebraic surfaces of type $K$3, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 530–572.