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Some inequalities for minimal fibrations of surfaces of general type over curves
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1992 Volume 44 Issue 4 Pages 643-666
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- Published: 1992 Received: April 24, 1991 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : A) S. Ju. Arakelov, Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk. SSSR, 35 (1971), 1277-1302.
Be1) A. Beauville, L'application canonique pour les surfaces de type général, Invent. Math., 55 (1979), 121-140.
Be2) A. Beauville, L'inégalité pg_??_2q-4 pour les surfaces de type général, Bull. Soc. Math. France, 110 (1982), 343-346.
Bo) E. Bombieri, Canonical models of surfaces of general type, Publ. Math. IHES, 42 (1973), 171-219.
De) O. Debarre, Inégalités numériques pour les surfaces de type général, Bull. Soc. Math. France, 110 (1982), 319-346.
E) R. Elkik, Rationalité des singularités canoniques, Invent. Math., 64 (1981), 1-6.
E-V) H. Esnault and E. Viehweg, Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields, Compositio Math., 76 (1990), 69-85.
F1) A. R. Fletcher, Contributions to Riemann-Rosh on projective 3-folds with only canonical singularities and applications, Proc. Sympos. Pure Math., 46 (1987), 221-231.
Fu) T. Fujita, On Kähler fiber spaces over curves, J. Math. Soc. Japan, 30 (1978), 779-794.
G) D. Gieseker, Global moduli for surfaces of general type, Invent. Math., 43 (1977), 233-282.
H-N) G. Harder and M. S. Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann., 212 (1975), 215-248.
Ha1) R. Hartshorne, Stable reflexive sheaves, Math. Ann., 254 (1980), 121-176.
Ha2) R. Hartshorne, Residues and Duality, LNM 20, Springer, 1966.
Ha3) R. Hartshorne, Algebraic Geometry, GTM 52, Springer, 1977.
Hi) H. Hironaka, Resolution of singularities of algebraic variety over a field of characteristic zero, I, Ann. of Math., 79 (1964), 109-203; II, Ann. of Math., 205-326.
Ho1) E. Horikawa, Algebraic surfaces of general type with small c21, I, Ann. of Math., 104 (1976), 357-387.
Ho2) E. Horikawa, Algebraic surfaces of general type with small c21, V, J. Fac. Sci. Univ. Tokyo Sect. A, 28 (1981), 745-755.
Hu) B. Hunt, Complex manifold geography in dimension 2 and 3, J. Differential Geom., 30 (1989), 51-153.
KMM) Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, in Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., 10, Kinokuniya, Tokyo and North-Holland Amsterdam, 1987, pp. 283-360.
Ka1) Y. Kawamata, Kodaira dimension of algebraic fiber spaces over curves, Invent. Math., 66 (1982), 57-71.
Ka2) Y. Kawamata, Minimal models and the Kodaira dimension of algebraic fiber spaces, J. Reine Angew. Math., 363 (1985), 1-46.
Ka3) Y. Kawamata, Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces, Ann. of Math., 127 (1988), 93-163.
Ko1) J. Kollár, Higher direct images of dualizing sheaves I, Ann. of Math., 123 (1986), 11-42.
Ko2) J. Kollár, Higher direct images of dualizing sheaves II, Ann, of Math., 124 (1986), 171-202.
Ko) M. Kobayashi, On Noether's inequality for threefolds, Master's thesis, Univ. of Tokyo, 1989.
N) N. Nakayama, Hodge filtrations and the higher direct images of canonical sheaves, Invent. Math., 85 (1986), 237-251.
Mi) Y. Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, in Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., 10, Kinokuniya, Tokyo and North-Holland Amsterdam, 1987, pp. 449-476.
Mo1) S. Mori, Classification of higher-dimensional varieties, Proc. of Sympos. Pure Math., 46 (1987), 269-331.
Mo2) S. Mori, Flip Theorem and the existence of minimal models for 3-folds, J. Amer. Math. Soc., 1 (1988), 117-253.
P) U. Persson, Chern invariants of surfaces of general type, Compositio Math., 43 (1981), 3-58.
R) M. Reid, Young person's guide to canonical singularities, Proc. of Sympos. Pure Math., 46 (1987), 345-414.
X) G. Xiao, Fibered algebraic surfaces with low slope, Math. Ann., 276 (1987), 449-466.
Right : [A] S. Ju. Arakelov, Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk. SSSR, 35 (1971), 1277-1302.
[Be1] A. Beauville, L'application canonique pour les surfaces de type général, Invent. Math., 55 (1979), 121-140.
[Be2] A. Beauville, L'inégalité pg≥2q-4 pour les surfaces de type général, Bull. Soc. Math. France, 110 (1982), 343-346.
[Bo] E. Bombieri, Canonical models of surfaces of general type, Publ. Math. IHES, 42 (1973), 171-219.
[De] O. Debarre, Inégalités numériques pour les surfaces de type général, Bull. Soc. Math. France, 110 (1982), 319-346.
[E] R. Elkik, Rationalité des singularités canoniques, Invent. Math., 64 (1981), 1-6.
[E-V] H. Esnault and E. Viehweg, Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields, Compositio Math., 76 (1990), 69-85.
[F1] A. R. Fletcher, Contributions to Riemann-Roch on projective 3-folds with only canonical singularities and applications, Proc. Sympos. Pure Math., 46 (1987), 221-231.
[Fu] T. Fujita, On Kähler fiber spaces over curves, J. Math. Soc. Japan, 30 (1978), 779-794.
[G] D. Gieseker, Global moduli for surfaces of general type, Invent. Math., 43 (1977), 233-282.
[H-N] G. Harder and M. S. Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann., 212 (1975), 215-248.
[Ha1] R. Hartshorne, Stable reflexive sheaves, Math. Ann., 254 (1980), 121-176.
[Ha2] R. Hartshorne, Residues and Duality, LNM 20, Springer, 1966.
[Ha3] R. Hartshorne, Algebraic Geometry, GTM 52, Springer, 1977.
[Hi] H. Hironaka, Resolution of singularities of algebraic variety over a field of characteristic zero, I, Ann. of Math., 79 (1964), 109-203; II, Ann. of Math., 205-326.
[Ho1] E. Horikawa, Algebraic surfaces of general type with small c21, I, Ann. of Math., 104 (1976), 357-387.
[Ho2] E. Horikawa, Algebraic surfaces of general type with small c21, V, J. Fac. Sci. Univ. Tokyo Sect. A, 28 (1981), 745-755.
[Hu] B. Hunt, Complex manifold geography in dimension 2 and 3, J. Differential Geom., 30 (1989), 51-153.
[KMM] Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, in Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., 10, Kinokuniya, Tokyo and North-Holland Amsterdam, 1987, pp. 283-360.
[Ka1] Y. Kawamata, Kodaira dimension of algebraic fiber spaces over curves, Invent. Math., 66 (1982), 57-71.
[Ka2] Y. Kawamata, Minimal models and the Kodaira dimension of algebraic fiber spaces, J. Reine Angew. Math., 363 (1985), 1-46.
[Ka3] Y. Kawamata, Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces, Ann. of Math., 127 (1988), 93-163.
[Ko1] J. Kollár, Higher direct images of dualizing sheaves I, Ann. of Math., 123 (1986), 11-42.
[Ko2] J. Kollár, Higher direct images of dualizing sheaves II, Ann, of Math., 124 (1986), 171-202.
[Ko] M. Kobayashi, On Noether's inequality for threefolds, Master's thesis, Univ. of Tokyo, 1989.
[N] N. Nakayama, Hodge filtrations and the higher direct images of canonical sheaves, Invent. Math., 85 (1986), 237-251.
[Mi] Y. Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, in Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., 10, Kinokuniya, Tokyo and North-Holland Amsterdam, 1987, pp. 449-476.
[Mo1] S. Mori, Classification of higher-dimensional varieties, Proc. of Sympos. Pure Math., 46 (1987), 269-331.
[Mo2] S. Mori, Flip Theorem and the existence of minimal models for 3-folds, J. Amer. Math. Soc., 1 (1988), 117-253.
[P] U. Persson, Chern invariants of surfaces of general type, Compositio Math., 43 (1981), 3-58.
[R] M. Reid, Young person's guide to canonical singularities, Proc. of Sympos. Pure Math., 46 (1987), 345-414.
[X] G. Xiao, Fibered algebraic surfaces with low slope, Math. Ann., 276 (1987), 449-466.
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