Zariski decomposition and canonical rings of elliptic threefolds

Takao FUJITA

doi:10.2969/jmsj/03810019

Takao FUJITA

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 1 Pages 19-37

DOI https://doi.org/10.2969/jmsj/03810019

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Published: 1986 Received: August 20, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : [E] R. Elkik, Rationallité des singularité canoniques, Invent. Math., 64 (1981), 1-6.
[F1] T. Fujita, On Zariski problem, Proc. Japan Acad., 55 (1979), 106-110.
[F2] T. Fujita, On L-dimension of coherent sheaves (with a correction), J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28 (1981), 215-236 & 29 (1982), 719-720.
[F3] T. Fujita, Semipositive line bundles, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 30 (1983), 353-378.
[F4]T. Fujita, Canonical rings of algebraic varieties, in Classification of Algebraic and Analytic Manifolds, ed. by K. Ueno, Progress in Math., 39, Birkhäuser, 1983.
[F5] T. Fujita, Fractionally logarithmic canonical rings of surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 30 (1984), 685-696.
[H1] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero I-II, Ann. of Math., 79 (1964), 109-326.
[H2] H. Hironaka, Introduction to the theory of infinitely near singular points, Memorias de Mat. del Inst. 'forge Juan', 28, Consejo Superior de Investigaciones Cientificas, Madrid, 1974.
[H3] H. Hironaka, Flattening theorem in complex-analytic geometry, Amer. J. Math., 97 (1975), 503-547.
[I] S. Iitaka, On D-dimensions of algebraic varieties, J. Math. Soc. Japan, 23 (1971), 356-373.
[Ka1] Y. Kawamata, Elementary contractions of algebraic 3-folds, preprint.
[Ka2] Y. Kawamata, Cone of curves of algebraic varieties, preprint.
[Ko1] K. Kodaira, On compact analytic surfaces II-III, Ann. of Math., 77 (1963), 563-626 & 78 (1963), 1-40.
[Ko2] K. Kodaira, On the structure of compact complex analytic surfaces, I, Amer. J. Math., 86 (1964), 751-798.
[R1] M. Reid, Canonical 3-folds, Geometrie Algebrique Angers 1979, A. Beauville ed., 1980, Sijthoff & Noordhoff, The Netherlands, 273-310.
[R2] M. Reid, Minimal model of canonical 3-folds, Advanced Studies in Pure Math., 1, Algebraic Varieties and Analytic Varieties, Kinokuniya, Tokyo & North-Holland, Amsterdam, 1983, 131-180.
[R3] M. Reid, Projective morphisms according to Kawamata, preprint.
[S] V. V. Shokurof, Theorem on non-vanishing (Russian), preprint.
[U1] K. Ueno, Classification of algebraic varieties I, Compositio Math., 27 (1973), 277-342.
[U2] K. Ueno, Classification Theory of Algebraic Varieties and Compact Complex Spaces, Lecture Notes in Math., 439, Springer, 1975
[Z] O. Zariski, The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface, Ann. of Math., 76 (1962), 560-615.

Right : [E] R. Elkik, Rationallité des singularité canoniques, Invent. Math., 64 (1981), 1-6.
[F1] T. Fujita, On Zariski problem, Proc. Japan Acad., 55 (1979), 106-110.
[F2] T. Fujita, On L-dimension of coherent sheaves (with a correction), J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28 (1981), 215-236 & 29 (1982), 719-720.
[F3] T. Fujita, Semipositive line bundles, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 30 (1983), 353-378.
[F4]T. Fujita, Canonical rings of algebraic varieties, in Classification of Algebraic and Analytic Manifolds, ed. by K. Ueno, Progress in Math., 39, Birkhäuser, 1983.
[F5] T. Fujita, Fractionally logarithmic canonical rings of surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 30 (1984), 685-696.
[H1] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero I-II, Ann. of Math., 79 (1964), 109-326.
[H2] H. Hironaka, Introduction to the theory of infinitely near singular points, Memorias de Mat. del Inst. ‘Jorge Juan’, 28, Consejo Superior de Investigaciones Cientificas, Madrid, 1974.
[H3] H. Hironaka, Flattening theorem in complex-analytic geometry, Amer. J. Math., 97 (1975), 503-547.
[I] S. Iitaka, On D-dimensions of algebraic varieties, J. Math. Soc. Japan, 23 (1971), 356-373.
[Ka1] Y. Kawamata, Elementary contractions of algebraic 3-folds, preprint.
[Ka2] Y. Kawamata, Cone of curves of algebraic varieties, preprint.
[Ko1] K. Kodaira, On compact analytic surfaces II-III, Ann. of Math., 77 (1963), 563-626 & 78 (1963), 1-40.
[Ko2] K. Kodaira, On the structure of compact complex analytic surfaces, I, Amer. J. Math., 86 (1964), 751-798.
[R1] M. Reid, Canonical 3-folds, Geometrie Algebrique Angers 1979, A. Beauville ed., 1980, Sijthoff & Noordhoff, The Netherlands, 273-310.
[R2] M. Reid, Minimal model of canonical 3-folds, Advanced Studies in Pure Math., 1, Algebraic Varieties and Analytic Varieties, Kinokuniya, Tokyo & North-Holland, Amsterdam, 1983, 131-180.
[R3] M. Reid, Projective morphisms according to Kawamata, preprint.
[S] V. V. Shokurof, Theorem on non-vanishing (Russian), preprint.
[U1] K. Ueno, Classification of algebraic varieties I, Compositio Math., 27 (1973), 277-342.
[U2] K. Ueno, Classification Theory of Algebraic Varieties and Compact Complex Spaces, Lecture Notes in Math., 439, Springer, 1975
[Z] O. Zariski, The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface, Ann. of Math., 76 (1962), 560-615.

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