Journal of Mathematical Sciences

, Volume 82, Issue 4, pp 3528–3613 | Cite as

Birational automorphisms of multidimensional algebraic manifolds

  • V. A. Iskovskikh
  • A. V. Pukhlikov


Manifold Algebraic Manifold Birational Automorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    M. H. Gizatulin, “RationalG-surfaces,”Izv. Akad. Nauk SSSR, Ser. Mat.,44, No. 1, 110–144 (1980).MathSciNetGoogle Scholar
  2. 2.
    M. H. Gizatulin, “The defining relations for the Cremona plane group,”Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 5, 909–970 (1982).MathSciNetGoogle Scholar
  3. 3.
    P. Griffiths and J. Harris,Principles of Algebraic Geometry, Wiley-Interscience, New York (1978).Google Scholar
  4. 4.
    V. A. Iskovskikh, “On birational automorphisms of algebraic 3-folds,”Dokl. Akad. Nauk SSSR,234, No. 4, 743–745 (1977).MATHMathSciNetGoogle Scholar
  5. 5.
    V. A. Iskovskikh, “Birational automorphisms of the Fano manifoldV 63,”Dokl. Akad. Nauk SSSR,235, No. 37, 509–511 (1977).MATHMathSciNetGoogle Scholar
  6. 6.
    V. A. Iskovskikh, “Birational automorphisms of algebraic 3-folds,” In:Sovremennye Problemy Matematik 12,Itogi Nauki i Tekhn., All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1979), pp. 159–236.Google Scholar
  7. 7.
    V. A. Iskovskikh, “Minimal models of rational surfaces over arbitrary fields,”Izv. Akad. Nauk SSSR, Ser. Mat.,43, No. 1, 19–43 (1979).MATHMathSciNetGoogle Scholar
  8. 8.
    V. A. Iskovskikh,Lectures on Algebraic 3-Folds. Fano Manifolds [In Russian], Moscow State University, Moscow (1988).Google Scholar
  9. 9.
    V. A. Iskovskikh, “Generators of the 2-dimensional Cremona group over a nonclosed field,”Tr. Mat. Inst. V. A. Steklova Akad. Nauk SSSR,200, 157–170 (1991).MATHGoogle Scholar
  10. 10.
    V. A. Iskovskikh and S. L. Tregub, “On birational automorphisms of rational surfaces,”Izv. Akad. Nauk SSSR, Ser. Mat.,55, No. 2, 254–283 (1991).MathSciNetGoogle Scholar
  11. 11.
    V. A. Iskovskikh, F. K. Kabdykairov, and S. L. Tregub, “Relations in the 2-dimensional Cremona group over perfect field,”Izv. Ros. Akad. Nauk, Ser. Mat.,57, No. 3, 3–69 (1993).MathSciNetGoogle Scholar
  12. 12.
    V. A. Iskovskikh and Y. I. Manin, “3-Dimensional quartics and counterexamples to the Luroth problem,”Mat. Sb.,86, No. 1, 140–166 (1971).MathSciNetGoogle Scholar
  13. 13.
    Y. I. Manin, “Rational surfaces over perfect fields,”Mat. Sb.,72, No. 2, 161–192 (1967).MATHMathSciNetGoogle Scholar
  14. 14.
    Y. I. Manin, “Correspondences, motives, and monoidal transformations,”Mat. Sb.,77, No. 4, 475–507 (1968).MATHMathSciNetGoogle Scholar
  15. 15.
    Y. I. Manin, “Lectures onK-functor in algebraic geometry,”Usp. Mat. Nauk,24, No. 5, 3–86 (1969).MATHMathSciNetGoogle Scholar
  16. 16.
    Y. I. Manin,Cubic Forms: Algebra, Geometry, Arithmetic [In Russian], Nauka, Moscow (1972).Google Scholar
  17. 17.
    A. V. Pukhlikov, “Birational automorphisms of 4-dimensional quintics,”Vestn. MGU, Ser. 1, No. 2, 10–15 (1986).MATHMathSciNetGoogle Scholar
  18. 18.
    A. V. Pukhlikov, “Birational automorphisms of a double space and double quadric,”Izv. Akad. Nauk SSSR, Ser. Mat.,52, No. 1, 229–239 (1988).Google Scholar
  19. 19.
    A. V. Pukhlikov, “Birational automorphisms of 3-dimensional quintics with the simplest singularity,”Mat. Sb.,135, No. 4, 472–496 (1988).MATHGoogle Scholar
  20. 20.
    A. V. Pukhlikov, “Maximal singularities on the Fano manifoldV 63,”Vestn. MGU, Ser. 1, No. 2, 47–50 (1989).MATHMathSciNetGoogle Scholar
  21. 21.
    V. G. Sarkisov, “Birational automorphisms of conic bundles,”Izv. Akad. Nauk SSSR, Ser. Mat.,44, No. 4, 918–944 (1980).MATHMathSciNetGoogle Scholar
  22. 22.
    V. G. Sarkisov, “On the structure of conic bundles,”Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 2, 371–408 (1982).MATHMathSciNetGoogle Scholar
  23. 23.
    V. G. Sarkisov,Classification of birational automorphisms of conic bundles 1. Associated cycles (Preprint Kurchatov Inst. Atomic Energy, No. 4446/15), Moscow (1987).Google Scholar
  24. 24.
    S. I. Hashin, “Birational automorphisms of a double 3-dimensional cone,”Vestn. MGU, Ser. 1, No. 1, 13–16 (1984).MATHGoogle Scholar
  25. 25.
    J. Collar,Nonrational hypersurfaces (Preprint) (1994).Google Scholar
  26. 26.
    A. Corti,Factoring birational maps of treefolds after Sarkisov (Preprint) (1992).Google Scholar
  27. 27.
    G. Fano, “Sopra alcune varieta algebriche a tre dimensioni aventa tutti i generi nulli,”Atti. Acc. Torino,43, 973–977 (1908).MATHGoogle Scholar
  28. 28.
    G. Fano, “Osservazioni sopra alcune varieta non razionali aventi tutti i generi nulli,”Atti. Acc. Torino,50, 1067–1072 (1915).MATHGoogle Scholar
  29. 29.
    G. Fano, “Sulle seczioni spaziali della varieta Grassmaniana delle rette spazio a cinque dimensioni,”Rend. R. Accad. Lincei.,11, No. 6, 329 (1930).MATHGoogle Scholar
  30. 30.
    G. Fano, “Nuove ricerche sulle varieta algebriche a tre dimensioni a curve-seczioni canoniche,”Comm. Rent. Ac. Sci.,11, 635–720 (1947).MATHMathSciNetGoogle Scholar
  31. 31.
    H. Hironaka, “Resolution of singularities of an algebraic variety over a field of characteristic zero,”Ann. Math.,79, No. 1-2, 109–326 (1964).MATHMathSciNetGoogle Scholar
  32. 32.
    H. P. Hudson,Cremona Transformations in Plane and Space, Cambridge Univ. Press, Cambridge (1927).Google Scholar
  33. 33.
    V. A. Iskovskikh and V. A. Pukhlikov, “Birational automorphisms of Fano varieties,” In:Geometry of Complex Projective Varieties, Mediterranean Press (1993), pp. 191–202.Google Scholar
  34. 34.
    A. V. Pukhlikov, “Birational isomorphisms of four-dimensional quintics,”Invent. Math.,87, 303–329 (1987).CrossRefMATHMathSciNetGoogle Scholar
  35. 35.
    M. Reid,Birational geometry of 3-folds according to Sarkisov (Preprint) (1991).Google Scholar
  36. 36.
    L. Roth,Algebraic Treefolds with Special Regard for the Problem of Rationality, Springer-Verlag, Berlin (1955).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. A. Iskovskikh
  • A. V. Pukhlikov

There are no affiliations available

Personalised recommendations