Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Birational invariants of rational surfaces

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

Literature cited

  1. 1.

    V. A. Iskovskikh, “Minimal models of rational surfaces over arbitrary fields,” Izv. Akad. Nauk SSSR, Ser. Mat.,43, No. 1, 19–43 (1979).

  2. 2.

    Yu. I. Manin, Cubic Forms [in Russian], Nauka, Moscow (1972).

  3. 3.

    B. É. Kunyavskii and M. A. Tsfasman, “Null-cycles on rational surfaces and tori of Neron-Severi,” Izv. Akad. Nauk. SSSR, Ser. Mat.,48, No. 3, 631–654 (1984).

  4. 4.

    Yu. I. Manin, “Rational surfaces over perfect fields. II,” Mat. Sb.,72, No. 2, 161–192 (1967).

  5. 5.

    V. A. Iskovskikh, “Rational surfaces with bundle of rational curves and positive square of the canonical class,” Mat. Sb.,83, No. 1, 90–119 (1970).

  6. 6.

    V. A. Iskovskikh, “Rational surfaces with bundle of rational curves,” Mat. Sb.,74, No. 4, 608–638 (1967).

  7. 7.

    V. A. Iskovskikh, “Birational properties of surfaces of degree 4 in P h 4 ,” Mat. Sb.,88, No. 1, 31–37 (1972).

  8. 8.

    J. Brzezinski, “Arithmetical quadratic surfaces of genus O. I.” Math. Scand.,46, 183–206 (1980).

  9. 9.

    V. A. Iskovskikh, “Generators and relations in groups of birational automorphisms of two classes of rational surfaces,” Trudy MIAN SSSR,165, 67–78 (1984).

  10. 10.

    N. Bourbaki, Lie Groups and Algebras [Russian translation], Mir, Moscow (1972), Chaps. IV–VI.

  11. 11.

    I. Naruki, “Cross ratio variety as a moduli space of cubic surfaces,” Proc. London Math. Soc.,45, No. 1, 1–30 (1982).

  12. 12.

    B. É. Kunyavskii, A. N. Skorobogatov, and M. A. Tsfasman, “Combinatorics and geometry of del Pezzo surfaces of degree 4,” Usp. Mat. Nauk,40, No. 6, 197–198 (1985).

Download references

Author information

Additional information

Translated from Matematicheskie Zametki, Vol. 39, No. 5, pp. 736–746, May, 1986.

The author thanks Yu. I. Manin, V. A. Iskovskikh, M. A. Tsfasman, B. É. Kunyavskii, and Zh. L. Kol'o-Telen for interest in the work.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Skorobogatov, A.N. Birational invariants of rational surfaces. Mathematical Notes of the Academy of Sciences of the USSR 39, 404–409 (1986). https://doi.org/10.1007/BF01156681

Download citation

Keywords

  • Rational Surface
  • Birational Invariant