New properties of special varieties arising from adjunction theory

Mauro C. BELTRAMETTI; Andrew J. SOMMESE

doi:10.2969/jmsj/04320381

Mauro C. BELTRAMETTI, Andrew J. SOMMESE

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 2 Pages 381-412

DOI https://doi.org/10.2969/jmsj/04320381

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Published: 1991 Received: December 05, 1989 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 : ACGH) E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris, Geometry of Algebraic Curves, Volume I, Grundlehren, 267, Springer-Verlag, 1985.
BPV) W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Ergebnisse der Math., 4, Springer-Verlag, 1984.
BV) A. Beauville, Surfaces algébriques complexes, Astérisque, 54, 1978.
BBS) M. Beltrametti, A. Biancofiore and A. J. Sommese, Projective N-folds of log-general type. I, Trans. Amer. Math. Soc., 314 (1989), 825-849.
BBS) M. Beltrametti, M. Schneider and A. J. Sommese, Threefolds of degree 9 and 10 in P⁵, Math. Ann., 288 (1990), 413-444.
B1) S. Bloch, Semiregularity and de Rham cohomology, Invent, Math., 17 (1972), 51-66.
D) A. Durfee, Fifteen characterizations of rational double points and simple critical points, Enseign. Math., 25 (1979), 131-163.
F) M. L. Fania, Configurations of -2 rational curves on sectional surfaces of n-folds, Math. Ann., 275 (1986), 317-325.
Fj) T. Fujita, On polarized manifolds whose adjoint bundles are not semipositive, Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., 10 (1987), 167-178.
FS) M. L. Fania and A. J. Sommese, On the minimality of hyperplane sections of Gorenstein threefolds, Contributions to several complex variables, in Honour of W. Stoll, Aspects of Math., E9, Vieweg-Verlag, 1986, 89-113.
Gr) H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331-368.
GP) L. Gruson and C. Peskine, Genre des courbes de l'espace projectif, Algebraic Geometry, Proceedings Tromsö, Norway 1977, Lecture Notes in Math., 687, Springer-Verlag, 1978.
H) R. Hartshorne, Algebraic Geometry, G. T. M., 52, Springer-Verlag, 1977.
I1) P. Ionescu, Embedded projective varieties of small invariants, Proceedings of the Week of Algebraic Geometry, Bucharest 1982, Lecture Notes in Math., 1056, Springer-Verlag, 1984, 142-187.
I2) P. Ionescu, Embedded projective varieties of small invariants, II, Rev. Roumaine Math. Pures Appl., 31 (1986), 539-544.
I3) P. Ionescu, Embedded projective varieties of small invariants, III, Preprint Series in Mathematics, 59 (1988), Bucharest.
M) S. Mori, Projective manifolds with ample tangent bundles, Ann, of Math., 110 (1979), 593-606.
N) S. Nakano, On the inverse of monoidal transformation, Publ. R. I. M. S., 6 (1971), 483-502.
O1) C. Okonek, 3-Mannigfaltigkeiten in P⁵ und ihre zugehörigen stabilen Garben, Manuscripta Math., 38 (1982), 175-199.
O2) C. Okonek, Über 2-codimensionale Untermannigfaltigkeiten vom Grad 7 in P⁴ und P⁵, Math. Zeit., 187 (1984), 209-219.
S1) A. J. Sommese, Hyperplane sections of projective surfaces, I-The adjunction mapping, Duke Math. J., 46 (1979), 377-401.
S2) A. J. Sommese, Hyperplane sections, Proceedings of the Algebraic Geometry Conference, University of Illinois at Chicago Circle, 1980, Lecture Notes in Math., 862, Springer-Verlag, 1981, 232-271.
S3) A. J. Sommese, On the minimality of hyperplane sections of projective threefolds, J. Reine Angew. Math., 329 (1981), 16-41.
S4) A. J. Sommese, On the birational theory of hyperplane sections of projective threefolds, Unpublished 1981 Manuscript.
S5) A. J. Sommese, Configurations of -2 rational curves on hyperplane sections of projective threefolds, Classification of Algebraic and Analytic Manifolds (ed. K. Ueno), Progr. Math., 39, Birkhäuser, 1983, 465-497.
S6) A. J. Sommese, Ample divisors on Gorenstein varieties, Proceedings of Complex Geometry Conference, Nancy 1985, Revue de I'Institut E. Cartan, 10 (1986).
S7) A. J. Sommese, On the adjunction theoretic structure of projective varieties, Complex Analysis and Algebraic Geometry, Proceedings Göttingen 1985, Lecture Notes in Math., 1194, Springer-Verlag, 1986, 175-213.
S8) A. J. Sommese, On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold, J. Reine Angew. Math., 402 (1989), 211-220; erratum, J. Reine Angew. Math., 41 (1990), 122-123.
SV) A. J. Sommese and A. Van de Ven, On the adjunction mapping, Math. Ann., 78 (1987), 593-603.
V) A. Van de Ven, On the 2-connectedness of very ample divisors on a surface, Duke Math. J., 46 (1979), 403-407.

Right : [ACGH] E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris, Geometry of Algebraic Curves, Volume I, Grundlehren, 267, Springer-Verlag, 1985.
[BPV] W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Ergebnisse der Math., 4, Springer-Verlag, 1984.
[Bv] A. Beauville, Surfaces algébriques complexes, Astérisque, 54, 1978.
[BBS] M. Beltrametti, A. Biancofiore and A. J. Sommese, Projective N-folds of loggeneral type. I, Trans. Amer. Math. Soc., 314 (1989), 825-849.
[BBS] M. Beltrametti, M. Schneider and A. J. Sommese, Threefolds of degree 9 and 10 in P⁵, Math. Ann., 288 (1990), 413-444.
[B1] S. Bloch, Semiregularity and de Rham cohomology, Invent, Math., 17 (1972), 51-66.
[D] A. Durfee, Fifteen characterizations of rational double points and simple critical points, Enseign. Math., 25 (1979), 131-163.
[F] M. L. Fania, Configurations of -2 rational curves on sectional surfaces of n-folds, Math. Ann., 275 (1986), 317-325.
[Fj] T. Fujita, On polarized manifolds whose adjoint bundles are not semipositive, Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., 10 (1987), 167-178.
[FS] M. L. Fania and A. J. Sommese, On the minimality of hyperplane sections of Gorenstein threefolds, Contributions to several complex variables, in Honour of W. Stoll, Aspects of Math., E9, Vieweg-Verlag, 1986, 89-113.
[Gr] H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331-368.
[GP] L. Gruson and C. Peskine, Genre des courbes de l'espace projectif, Algebraic Geometry, Proceedings Tromsö, Norway 1977, Lecture Notes in Math., 687, Springer-Verlag, 1978.
[H] R. Hartshorne, Algebraic Geometry, G. T. M., 52, Springer-Verlag, 1977.
[I1] P. Ionescu, Embedded projective varieties of small invariants, Proceedings of the Week of Algebraic Geometry, Bucharest 1982, Lecture Notes in Math., 1056, Springer-Verlag, 1984, 142-187.
[I2] P. Ionescu, Embedded projective varieties of small invariants, II, Rev. Roumaine Math. Pures Appl., 31 (1986), 539-544.
[I3] P. Ionescu, Embedded projective varieties of small invariants, III, Preprint Series in Mathematics, 59 (1988), Bucharest.
[M] S. Mori, Projective manifolds with ample tangent bundles, Ann, of Math., 110 (1979), 593-606.
[N] S. Nakano, On the inverse of monoidal transformation, Publ. R. I. M. S., 6 (1971), 483-502.
[O1] C. Okonek, 3-Mannigfaltigkeiten in P⁵ und ihre zugehörigen stabilen Garben, Manuscripta Math., 38 (1982), 175-199.
[O2] C. Okonek, Über 2-codimensionale Untermannigfaltigkeiten vom Grad 7 in P⁴ und P⁵, Math. Zeit., 187 (1984), 209-219.
[S1] A. J. Sommese, Hyperplane sections of projective surfaces, I-The adjunction mapping, Duke Math. J., 46 (1979), 377-401.
[S2] A. J. Sommese, Hyperplane sections, Proceedings of the Algebraic Geometry Conference, University of Illinois at Chicago Circle, 1980, Lecture Notes in Math., 862, Springer-Verlag, 1981, 232-271.
[S3] A. J. Sommese, On the minimality of hyperplane sections of projective threefolds, J. Reine Angew. Math., 329 (1981), 16-41.
[S4] A. J. Sommese, On the birational theory of hyperplane sections of projective threefolds, Unpublished 1981 Manuscript.
[S5] A. J. Sommese, Configurations of -2 rational curves on hyperplane sections of projective threefolds, Classification of Algebraic and Analytic Manifolds (ed. K. Ueno), Progr. Math., 39, Birkhäuser, 1983, 465-497.
[S6] A. J. Sommese, Ample divisors on Gorenstein varieties, Proceedings of Complex Geometry Conference, Nancy 1985, Revue de I'Institut E. Cartan, 10 (1986).
[S7] A. J. Sommese, On the adjunction theoretic structure of projective varieties, Complex Analysis and Algebraic Geometry, Proceedings Göttingen 1985, Lecture Notes in Math., 1194, Springer-Verlag, 1986, 175-213.
[S8] A. J. Sommese, On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold, J. Reine Angew. Math., 402 (1989), 211-220; erratum, J. Reine Angew. Math., 41 (1990), 122-123.
[SV] A. J. Sommese and A. Van de Ven, On the adjunction mapping, Math. Ann., 278 (1987), 593-603.
[V] A. Van de Ven, On the 2-connectedness of very ample divisors on a surface, Duke Math. J., 46 (1979), 403-407.

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