Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Projective $ n$-folds of log-general type. I


Authors: M. Beltrametti, A. Biancofiore and A. J. Sommese
Journal: Trans. Amer. Math. Soc. 314 (1989), 825-849
MSC: Primary 14J40; Secondary 14C20, 14J30
MathSciNet review: 1005528
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Abstract: Let $ X$ be a normal $ n$-dimensional Gorenstein irreducible projective subvariety of a complex projective space with codimension $ 3$ singularities. This article introduces new projective invariants of $ X$ and shows that they satisfy certain inequalities and relations making them useful tools in the projective classification of varieties. The main tools used are the recent precise adjunction theoretic results on classification of projective varieties.


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  • [Ba-P-V] W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574
  • [Bo] E. Bombieri, Canonical models of surfaces of general type, Inst. Hautes Études Sci. Publ. Math. 42 (1973), 171–219. MR 0318163
  • [Be] A. Beauville, Letter on Reider's method, March 17, 1986.
  • [Fa-So] Maria Lucia Fania and Andrew John Sommese, On the minimality of hyperplane sections of Gorenstein threefolds, Contributions to several complex variables, Aspects Math., E9, Vieweg, Braunschweig, 1986, pp. 89–113. MR 859194
  • [Fj] Takao Fujita, On polarized manifolds whose adjoint bundles are not semipositive, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 167–178. MR 946238
  • [Fl] William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620
  • [Fl-La] William Fulton and Robert Lazarsfeld, Connectivity and its applications in algebraic geometry, Algebraic geometry (Chicago, Ill., 1980) Lecture Notes in Math., vol. 862, Springer, Berlin-New York, 1981, pp. 26–92. MR 644817
  • [H] Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157
  • [I-Sh] V. A. Iskovskih and V. V. Shokurov, Biregular theory of Fano $ 3$-folds, Proceedings, Copenhagen 1978, Lecture Notes in Math., vol. 732, Springer-Verlag, New York, 1979.
  • [L-M] D. Lieberman and D. Mumford, Matsusaka’s big theorem, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 513–530. MR 0379494
  • [Li-So] Elvira Laura Livorni and Andrew John Sommese, Threefolds of nonnegative Kodaira dimension with sectional genus less than or equal to 15, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1986), no. 4, 537–558. MR 880398
  • [R] L. Roth, On the projective classification of surfaces, Proc. London Math. Soc. (2) 42 (1937), 142-170.
  • [So1] Andrew John Sommese, Submanifolds of Abelian varieties, Math. Ann. 233 (1978), no. 3, 229–256. MR 0466647
  • [So2] -, Configurations of $ - 2$ rational curves on hyperplane sections of projective threefolds, Classification of Algebraic and Analytic Manifolds, Progress in Math., vol. 39, Birkhäuser-Verlag, 1980, pp. 465-497.
  • [So3] Andrew John Sommese, Hyperplane sections, Algebraic geometry (Chicago, Ill., 1980) Lecture Notes in Math., vol. 862, Springer, Berlin-New York, 1981, pp. 232–271. MR 644822
  • [So4] Andrew John Sommese, On the minimality of hyperplane sections of projective threefolds, J. Reine Angew. Math. 329 (1981), 16–41. MR 636441, 10.1515/crll.1981.329.16
  • [So5] Andrew John Sommese, Complex subspaces of homogeneous complex manifolds. II. Homotopy results, Nagoya Math. J. 86 (1982), 101–129. MR 661221
  • [So6] A. J. Sommese, Ample divisors on normal Gorenstein surfaces, Abh. Math. Sem. Univ. Hamburg 55 (1985), 151–170. MR 831524, 10.1007/BF02941494
  • [So7] Andrew John Sommese, On the adjunction theoretic structure of projective varieties, Complex analysis and algebraic geometry (Göttingen, 1985) Lecture Notes in Math., vol. 1194, Springer, Berlin, 1986, pp. 175–213. MR 855885, 10.1007/BFb0077004

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DOI: http://dx.doi.org/10.1090/S0002-9947-1989-1005528-1
Article copyright: © Copyright 1989 American Mathematical Society