On Noether's inequality for threefolds

Masanori KOBAYASHI

doi:10.2969/jmsj/04410145

Masanori KOBAYASHI

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 1 Pages 145-156

DOI https://doi.org/10.2969/jmsj/04410145

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Published: 1992 Received: March 14, 1990 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 : Be) A Beauville, L'application canonique pour les surfaces de type général, Invent. Math., 55 (1979), 121-140.
Bo) E. Bombieri, Canonical models of surfaces of general type, Publ. I. H. E. S., 42 (1973), 171-219.
BPV) W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Springer-Verlag, Berlin, Heidelberg, 1984.
C) G. Castelnuovo, Intorno alla geometria sopra una superficie algebrica, Nota II, Osservazioni, Rendiconti del R. Istituto Lombardo, s. II, 24 (1891), 307-318.
E) F. Enriques, Le Superficie algebriche, Bologne, Zanichelli, 1949.
F1) T. Fujita, On the structure of polarized varieties of Δ-genera 0, J. Fac. Sci. Univ. Tokyo, 22 (1975), 103-115.
F2) T. Fujita, On hyperelliptic polarized varieties, Tohoku Math., 35 (1984), 1-44.
F3) T. Fujita, On polarized manifolds of Δ-genus two, part I, J. Math. Soc. Japan, 36 (1984), 709-730.
H1) E. Horikawa, Algebraic surfaces of general type with small c²₁ I, Ann. of Math. 104 (1976), 357-387; II, Invent. Math., 37 (1976), 121-155; III, Invent. Math., 47 (1978), 209-248; IV, Invent. Math., 50 (1979), 103-128; V, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28 (1982), 745-755.
H2) E. Horikawa, Regular threefolds with trivial canonical bundle, Recent Topics in Algebraic Geometry, RIMS, Kokyuroku, 409 (1980), 39-45, (in Japanese).
H3) E. Horikawa, Regular threefolds with trivial canonical bundle, Recent Topics in Algebraic Geometry, RIMS., Kaisekitayotai-seminar kinoku, Univ. of Tokyo, (1981), notes on 1/17 (in Japanese).
Ha) R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.
Hi) H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, I, Ann, of Math., 79 (1964), 109-203, II, Ann, of Math., 205-326.
Hu) B. Hunt, Complex manifold geography in dimension 2 and 3, J. Diff. Geom., 30 (1989), 51-153.
K) Y. Kawamata, Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces, Ann. of Math., 127 (1988), 93-163.
KMM) Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, in Algebraic geometry, Sendai 1985, Adv. Stud. in Pure Math., 10, Kinokuniya, Tokyo and North-Holland Amsterdam, 1987, pp. 283-360.
R) M. Reid, Minimal Models of Canonical 3-folds, in Algebraic Varieties and Analytic Varieties, Adv. Stud. in Pure Math. 1, Kinokuniya, Tokyo and North-Holland, Amsterdam, 1983, pp. 131-180.

Right : [Be] A Beauville, L'application canonique pour les surfaces de type général, Invent. Math., 55 (1979), 121-140.
[Bo] E. Bombieri, Canonical models of surfaces of general type, Publ. I. H. E. S., 42 (1973), 171-219.
[BPV] W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Springer-Verlag, Berlin, Heidelberg, 1984.
[C] G. Castelnuovo, Intorno alla geometria sopra una superficie algebrica, Nota II, Osservazioni, Rendiconti del R. Istituto Lombardo, s. II, 24 (1891), 307-318.
[E] F. Enriques, Le Superficie algebriche, Bologne, Zanichelli, 1949.
[F1] T. Fujita, On the structure of polarized varieties of Δ-genera 0, J. Fac. Sci. Univ. Tokyo, 22 (1975), 103-115.
[F2] T. Fujita, On hyperelliptic polarized varieties, Tôhoku Math., 35 (1984), 1-44.
[F3] T. Fujita, On polarized manifolds of Δ-genus two, part I, J. Math. Soc. Japan, 36 (1984), 709-730.
[H1] E. Horikawa, Algebraic surfaces of general type with small c²₁ I, Ann. of Math. 104 (1976), 357-387; II, Invent. Math., 37 (1976), 121-155; III, Invent. Math., 47 (1978), 209-248; IV, Invent. Math., 50 (1979), 103-128; V, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28 (1982), 745-755.
[H2] E. Horikawa, Regular threefolds with trivial canonical bundle, Recent Topics in Algebraic Geometry, RIMS, Kokyuroku, 409 (1980), 39-45, (in Japanese).
[H3] E. Horikawa, Regular threefolds with trivial canonical bundle, Recent Topics in Algebraic Geometry, RIMS., Kaisekitayôtai-seminar kinoku, Univ. of Tokyo, (1981), notes on 1/17 (in Japanese).
[Ha] R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.
[Hi] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, I, Ann, of Math., 79 (1964), 109-203, II, Ann, of Math., 205-326.
[Hu] B. Hunt, Complex manifold geography in dimension 2 and 3, J. Diff. Geom., 30 (1989), 51-153.
[K] Y. Kawamata, Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces, Ann. of Math., 127 (1988), 93-163.
[KMM] Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, in Algebraic geometry, Sendai 1985, Adv. Stud. in Pure Math., 10, Kinokuniya, Tokyo and North-Holland Amsterdam, 1987, pp. 283-360.
[R] M. Reid, Minimal Models of Canonical 3-folds, in Algebraic Varieties and Analytic Varieties, Adv. Stud. in Pure Math. 1, Kinokuniya, Tokyo and North-Holland, Amsterdam, 1983, pp. 131-180.

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