Nagoya Mathematical Journal

Algebraic deformations of polarized varieties

T. Matsusaka

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 31 (1968), 185-245.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118796947

Mathematical Reviews number (MathSciNet)
MR0258827

Zentralblatt MATH identifier
0167.49501

Subjects
Primary: 14.15

Citation

Matsusaka, T. Algebraic deformations of polarized varieties. Nagoya Math. J. 31 (1968), 185--245. https://projecteuclid.org/euclid.nmj/1118796947


Export citation

References

  • [1] W.L. Chow, On the connectedness theorem, in algebraic geometry, American Journal of Mathematics, vol. 81, (1959), pp. 1033-1074.
  • [2] W.L. Chow, Algebraic systems of positive cycles in an algebraic variety, American Journal of Mathematics, vol. 72, (1950), pp. 247-283.
  • [3] W.L. Chow-v.d. Waerden, Zur algebraischen Geometrie IX, MathematischeAnnalen, vol. 113, (1937), pp. 692-704.
  • [4] A. Grothendieck, Elements de geometrie algebriques, I-IV, Publications Mathematiques Institut des Hautes Etudes Scientiiques, Paris.
  • [5] A. Grothendieck, Les schemas de Hubert, Seminaire Bourbaki, n 221, (1960/61).
  • [6] A. Grothendieck, Les schemas de Picard Proprites genrales, Seminaire Bourbaki, n 236, (1961/62).
  • [7] H. Hironaka, A note on algebraic geometry over ground rings, Illinois Journal of Mathematics, vol. 2 (1958), pp. 355-366.
  • [8] W.V.D. Hodge,The theory and applications of harmonic integrals, Cambridge University Press (1959).
  • [8'] S. Kleiman, Toward a numerical theory of ampleness, Thesis at Harvard University (1965).
  • [9] K. Kodaira and D.C. Spencer, On deformations of complex analytic Structures, I,II, Annals of Mathematics, vol. 67 (1958), pp. 328-466.
  • [10] S. Lang, Abelian varieties, Interscience Tracts, No. 7, 1959.
  • [11] T. Matsusaka, On the algebraic construction of the Picard variety, II, Japanese Journal of Mathematics, vol. 22 (1952), pp. 51-62.
  • [12] T. Matsusaka, Onthealgebraic families ofpositive divisors,Journal ofthe Mathema- tical Society ofJapan, vol.5 (1953), pp. 115-136.
  • [13] T. Matsusaka, The criteria for algebraic equivalence andthetorsion group, American Journal of Mathematics, vol.79 (1957), pp. 53-66.
  • [14] T. Matsusaka, Polarized varieties, fields ofmoduli, etc.,AmericanJournal ofMathema- tics, vol.80 (1958), pp.45-82.
  • [15] T. Matsusaka, Theory ofQ-varieties, Publications ofthe Mathematical Society ofJapan, No. 8, 1965.
  • [16] T.Matsusaka andD. Mumford, Two fundamental theorems ondeformations ofpolarized varieties, American Journal of Mathematics, vol. 86 (1964), pp. 668-684.
  • [17] D. Mumford, Geometric invariant theory, Berlin-Heidelberg-New York Springer,1965.
  • [18] Y.Nakai, Note ontheintersection ofan algebraic variety with thegeneric hyperplane, Memoirs of the College of Science, Kyoto University,vol. 26 (1951), pp. 185-187.
  • [19] S.Lang andA.Neron, Rational points ofAbelian varieties over function fields, Ameri- can Journal of Mathematics, vol. 81 (1959), pp. 95-118.
  • [20] J.-p. Serre, Faisceaux algebriques coherents, Annals of Mathematics, vol. 61(1955), pp. 197-278.
  • [21] G. Shimura, Reduction ofalgebraic varieties with respect to a discrete valuation of the basis field, American Journal of Mathematics, vol.77 (1955), pp. 134-176.
  • [22] G. Shimura, Modules des varietes abeliennes polarisees et fonctions modulaires, Seminaire H. Cartan, E.N.S. (1957/58).
  • [22'] E. Snapper, Multiples of divisors, Journal of Mathematics and Mechanics, vol.8 (1959), pp.967–992.
  • [23] A.Weil, Foundations ofalgebraic geometry, American Mathematical Society Colloquium Publications, No.29 (1960).
  • [24] A.Weil, On algebraic groups of transformations, American Journal of Mathematics, Vol. 77 (1955), pp.355-391.
  • [25] A.Weil, On the theory of complex multiplications, Proceedings, International Sym- posium onAlgebraic Number Theory, Nikko, Japan,1955.
  • [26] O. Zariski, Scientific report on the second summer institute, III, Bulletin ofthe American Mathematical Society, Vol.62 (1956), pp. 117-141.
  • [27] Complete linear systems onnormal varieties anda generalization ofalemma of Enriques-Severi, Annals of Mathematics, Vol.55 (1952), pp.552-592. Brandeis University

See also

  • See also: T. Matsusaka. Correction 1: "Algebraic deformations of polarized varieties". Nagoya Mathematical Journal vol. 33, (1968), pp. 137-137.
  • See also: T. Matsusaka. Correction 2: "Algebraic deformations of polarized varieties". Nagoya Mathematical Journal Volume 36, (1969), pp. 119-119.