A lower bound for sectional genus of quasi-polarized manifolds

Yoshiaki FUKUMA

doi:10.2969/jmsj/04920339

Yoshiaki FUKUMA

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 2 Pages 339-362

DOI https://doi.org/10.2969/jmsj/04920339

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Published: 1997 Received: August 18, 1994 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 : B-G) S. Bloch and D. Gieseker, The positivity of the Chern classes of an ample vector bundle, Invent. Math., 12 (1971), 112-117.
BPV) W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces, 1984, Springer-Verlag.
EGA) J. Dieudonné and A. Grothendieck, Eléments de Géométrie Algébrique, Publ. Math. Inst. HES., 4, 8,11,17, 20, 24, 28, 32.
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.
F-R) T. Fujita and J. Roberts, Varieties with small secant varieties: extremal case, Amer. J. Math., 103 (1981), 953-976.
Fj1) T. Fujita, On Kähler fiber spaces over curves, J. Math. Soc. Japan, 30 (1978), 779-794.
Fj2) T. Fujita, On polarized manifolds whose adjoint bundles are not semipositive, in Algebraic Geometry, Sendai 1985, Adv. Stud. Pure Math., 10 (1987), 167-178.
Fj3) T. Fujita, Classification Theories of Polarized Varieties, London Math. Soc. Lecture Note Ser., 155, 1990, Cambridge.
Fk1) Y. Fukuma, A lower bound for the sectional genus of quasi-polarized surfaces, to appear in Geom. Dedicata.
Fk2) Y. Fukuma, Master Thesis (in Japanese), (1993).
H-N) G. Harder and M. S. Narashimhan, On the cohomology groups of rnoduli spaces of vector bundles on curves, Math. Ann., 212 (1975), 215-248.
Ha1) R, Hartshorne, Algebraic Geometry, Graduate Texts in Math., 52, Springer-Verlag, New York, Heidelberg, Berlin, 1977.
Ha2) R. Hartshorne, Ample subvarieties of Algebraic Varieties, Lecture Notes in Math., 156, 1986, Springer-Verlag.
Hi) H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero I, II, Ann. of Math., 79 (1964), 109-326.
Ii1) S. Iitaka, On D-dimension of algebraic varieties, J. Math. Soc. Japan, 23 (1971), 356-373.
Ii2) S. Iitaka, Algebraic Geometry, Graduate Texts in Math., 76, Springer-Verlag, New York, Heidelberg, Berlin, 1982.
Io) P. Ionescu, Generalized adjunction and applications, Math. Proc. Cambridge Philos. Soc., 99 (1986), 457-472.
KMM) Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, in Algebraic Geometry, Sendai 1985, Adv. Stud. Pure Math., 10 (1987), 283-360.
Ka1) Y. Kawamata, Characterization of Abelian varieties, Compositio Math., 43 (1981), 253-276.
Ka2) Y. Kawamata, Kodaira dimension of algebraic fiber spaces over curves, Invent. Math., 66 (1982), 59-71.
L-P) A. Lanteri and M. Palleschi, About the adjunction process for polarized algebraic surfaces, J. Reine Angew. Math., 352 (1984), 15-23.
Mh) K. Maehara, The weak 1-positivity of direct image sheaves, J. Reine Angew. Math., 364 (1986), 112-129.
Mo) S. Mori, Classification of higher-dimensional varieties, in Algebraic Geometry, Bowdoin 1985, Proc. Sympos. Pure Math., 46 (1987), 269-331.
Mu) D. Mumford, Algebraic Geometry I Complex projective varieties, 1970, Springer-Verlag.
O) K. Ohno, Some inequalities for minimal fibrations of surfaces of general types over curves, J. Math. Soc. Japan, 44 (1992), 643-666.
U) K. Ueno, Classification Theory of Algebraic Varieties, Lecture Notes in Math., 439, 1975, Springer-Verlag.
V1) E. Viehweg, Rational singularity of higher dimensional schemes, Proc. Amer. Math. Soc., 63 (1977), 6-8.
V2) E. Viehweg, Klassifikationstheorie algebraischer varietäten der dimension drei, Compositio Math., 41 (1980), 361-400.
V3) E. Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fiber spaces, Adv. Stud. Pure Math., 1 (1983), 329-353.

Right : [B-G] S. Bloch and D. Gieseker, The positivity of the Chern classes of an ample vector bundle, Invent. Math., 12 (1971), 112-117.
[BPV] W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces, 1984, Springer-Verlag.
[EGA] J. Dieudonné and A. Grothendieck, Eléments de Géométrie Algébrique, Publ. Math. Inst. HES., 4, 8, 11, 17, 20, 24, 28, 32.
[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.
[F-R] T. Fujita and J. Roberts, Varieties with small secant varieties: extremal case, Amer. J. Math., 103 (1981), 953-976.
[Fj1] T. Fujita, On Kähler fiber spaces over curves, J. Math. Soc. Japan, 30 (1978), 779-794.
[Fj2] T. Fujita, On polarized manifolds whose adjoint bundles are not semipositive, in Algebraic Geometry, Sendai 1985, Adv. Stud. Pure Math., 10 (1987), 167-178.
[Fj3] T. Fujita, Classification Theories of Polarized Varieties, London Math. Soc. Lecture Note Ser., 155, 1990, Cambridge.
[Fk1] Y. Fukuma, A lower bound for the sectional genus of quasi-polarized surfaces, to appear in Geom. Dedicata.
[Fk2] Y. Fukuma, Master Thesis (in Japanese), (1993).
[H-N] G. Harder and M. S. Narashimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann., 212 (1975), 215-248.
[Ha1] R, Hartshorne, Algebraic Geometry, Graduate Texts in Math., 52, Springer-Verlag, New York, Heidelberg, Berlin, 1977.
[Ha2] R. Hartshorne, Ample subvarieties of Algebraic Varieties, Lecture Notes in Math., 156, 1986, Springer-Verlag.
[Hi] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero I, II, Ann. of Math., 79 (1964), 109-326.
[Ii1] S. Iitaka, On D-dimension of algebraic varieties, J. Math. Soc. Japan, 23 (1971), 356-373.
[Ii2] S. Iitaka, Algebraic Geometry, Graduate Texts in Math., 76, Springer-Verlag, New York, Heidelberg, Berlin, 1982.
[Io] P. Ionescu, Generalized adjunction and applications, Math. Proc. Cambridge Philos. Soc., 99 (1986), 457-472.
[KMM] Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, in Algebraic Geometry, Sendai 1985, Adv. Stud. Pure Math., 10 (1987), 283-360.
[Ka1] Y. Kawamata, Characterization of Abelian varieties, Compositio Math., 43 (1981), 253-276.
[Ka2] Y. Kawamata, Kodaira dimension of algebraic fiber spaces over curves, Invent. Math., 66 (1982), 59-71.
[L-P] A. Lanteri and M. Palleschi, About the adjunction process for polarized algebraic surfaces, J. Reine Angew. Math., 352 (1984), 15-23.
[Mh] K. Maehara, The weak 1-positivity of direct image sheaves, J. Reine Angew. Math., 364 (1986), 112-129.
[Mo] S. Mori, Classification of higher-dimensional varieties, in Algebraic Geometry, Bowdoin 1985, Proc. Sympos. Pure Math., 46 (1987), 269-331.
[Mu] D. Mumford, Algebraic Geometry I Complex projective varieties, 1970, Springer-Verlag.
[O] K. Ohno, Some inequalities for minimal fibrations of surfaces of general types over curves, J. Math. Soc. Japan, 44 (1992), 643-666.
[U] K. Ueno, Classification Theory of Algebraic Varieties, Lecture Notes in Math., 439, 1975, Springer-Verlag.
[V1] E. Viehweg, Rational singularity of higher dimensional schemes, Proc. Amer. Math. Soc., 63 (1977), 6-8.
[V2] E. Viehweg, Klassifikationstheorie algebraischer varietäten der dimension drei, Compositio Math., 41 (1980), 361-400.
[V3] E. Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fiber spaces, Adv. Stud. Pure Math., 1 (1983), 329-353.

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