On some new birational invariants of algebraic varieties and their application to rationality of certain algebraic varieties of dimension 3

Shigeru IITAKA

doi:10.2969/jmsj/02430384

Shigeru IITAKA

著者情報

ジャーナルフリー

1972 年 24 巻 3 号 p. 384-396

DOI https://doi.org/10.2969/jmsj/02430384

詳細

Published: 1972 Received: 1970/12/12 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : Shigeru IITAKA¹⁾
Right : Shigeru IITAKA¹⁾²⁾

訂正日: 2006/09/29 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Department of Mathematics University of Tokyo and The Institute for Advanced Study Princeton

訂正後 :
1) Department of Mathematics University of Tokyo
2) The Institute for Advanced Study Princeton

訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) S. Abhyanker, On the valuation centered in a local domain, Amer. J. Math., 78 (1955), 321-348.
2) T. T. Frankel, Manifolds with positive curvature, Pacific J. Math., 11 (1961), 165-178.
3) R. Hartshorne, Ample vector bundles, Publ. Math. de I. H. E. S., No. 29 (1966), 319-349.
4) H. Hironaka, Resolution of singularity of an algebraic variety of characteristic zero I, II, Ann. of Math., 79 (1964), 109-326.
5) H. Hironaka, Resolution of singularities of a complex variety (French), to appear.
6) S. Iitaka, Deformations of compact complex surfaces II, III, J. Math. Soc. Japan, 22 (1970), 247-261; 23 (1971), 692-705.
7) S. Iitaka, On D-dimensions of algebraic varieties, J. Math. Soc. Japan, 23 (1971), 356-373.
8) S. Iitaka, Genera and classifications of algebraic varieties (Japanese), Sugaku, 24 (1972), 14-27.
9) S. Iitaka, Classification of algebraic varieties (Korean), Study in Mathematics and Statistics (Dankook University), 4 (1971), 7-19.
10) S. Kobayashi and T. Ochiai, On complex manifolds with positive tangent bundles, J. Math. Soc. Japan, 22 (1970), 499-525.
11) S. Kobayashi and T. Ochiai, Three-dimensional compact Kähler manifolds with positive holomorphic bisectional curvature, J. Math. Soc. Japan, 24 (3) (1972).
12) K. Kodaira, On the structure of compact complex analytic surfaces I, II, III, IV, Amer. J. Math., 86 (1964), 751-798; 88 (1966), 687-721; 90 (1968), 55-83; 90 (1968), 1048-1066.
13) H. Matsumura, On algebraic groups of birational transformations, Lincei-Rend. Sc. fis. Mat. e nat., 34 (1963), 151-155.
14) L. Roth, Algebraic Threefolds, Springer-Verlag, Berlin, 1955.
15) F. Severi, Le equivalenze algebriche, Rend. Accad. Linc., (8) 18 (1955), 357-361.
16) O. Zariski, Introduction to the problem of minimal models in the theory of algebraic surfaces, Publ. Math. Soc. Japan, No. 4, Tokyo, 1958.

Right : [1] S. Abhyanker, On the valuation centered in a local domain, Amer. J. Math., 78 (1955), 321-348.
[2] T. T. Frankel, Manifolds with positive curvature, Pacific J. Math., 11 (1961), 165-178.
[3] R. Hartshorne, Ample vector bundles, Publ. Math. de I. H. E. S., No. 29 (1966), 319-349.
[4] H. Hironaka, Resolution of singularity of an algebraic variety of characteristic zero I, II, Ann. of Math., 79 (1964), 109-326.
[5] H. Hironaka, Resolution of singularities of a complex variety (French), to appear.
[6] S. Iitaka, Deformations of compact complex surfaces II, III, J. Math. Soc. Japan, 22 (1970), 247-261; 23 (1971), 692-705.
[7] S. Iitaka, On D-dimensions of algebraic varieties, J. Math. Soc. Japan, 23 (1971), 356-373.
[8] S. Iitaka, Genera and classifications of algebraic varieties (Japanese), Sugaku, 24 (1972), 14-27.
[9] S. Iitaka, Classification of algebraic varieties (Korean), Study in Mathematics and Statistics (Dankook University), 4 (1971), 7-19.
[10] S. Kobayashi and T. Ochiai, On complex manifolds with positive tangent bundles, J. Math. Soc. Japan, 22 (1970), 499-525.
[11] S. Kobayashi and T. Ochiai, Three-dimensional compact Kähler manifolds with positive holomorphic bisectional curvature, J. Math. Soc. Japan, 24 (3) (1972).
[12] K. Kodaira, On the structure of compact complex analytic surfaces I, II, III, IV, Amer. J. Math., 86 (1964), 751-798; 88 (1966), 687-721; 90 (1968), 55-83; 90 (1968), 1048-1066.
[13] H. Matsumura, On algebraic groups of birational transformations, Lincei-Rend. Sc. fis. Mat. e nat., 34 (1963), 151-155.
[14] L. Roth, Algebraic Threefolds, Springer-Verlag, Berlin, 1955.
[15] F. Severi, Le equivalenze algebriche, Rend. Accad. Linc., (8) 18 (1955), 357-361.
[16] O. Zariski, Introduction to the problem of minimal models in the theory of algebraic surfaces, Publ. Math. Soc. Japan, No. 4, Tokyo, 1958.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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