Geodesic
On the Nonemptiness of the Adjoint Linear System of Polarized Manifolds
Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 267-278

Voir la notice de l'article provenant de la source Cambridge University Press

Let $(X,L)$ be a polarized manifold over the complex number field with dim $X=n$ . In this paper, we consider a conjecture of M. C. Beltrametti and A. J. Sommese and we obtain that this conjecture is true if $n=3$ and ${{h}^{0}}\,(L)\,\ge \,2$ , or $\dim\,\text{Bs}|L|\le 0$ for any $n\ge 3$ . Moreover we can generalize the result of Sommese.
DOI : 10.4153/CMB-1998-039-9
Mots-clés : 14C20, 14J99, Polarized manifold, adjoint bundle 
Fukuma, Yoshiaki. On the Nonemptiness of the Adjoint Linear System of Polarized Manifolds. Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 267-278. doi: 10.4153/CMB-1998-039-9
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[BS] [BS] Beltrametti, M. C. and Sommese, A. J., The adjunction theory of complex projective varieties. de Gruyter Expositions in Math. 16, Walter de Gruyter, Berlin, New York. Google Scholar

[Fj0] [Fj0] Fujita, T., Classification Theories of Polarized Varieties. London Math. Soc. Lecture Note Series 155 (1990). Google Scholar

[Fj1] [Fj1] Fujita, T., On polarized manifolds whose adjoint bundles are not semipositive. Adv. Stud. Pure Math. 10 (1985), 167–178. Google Scholar

[Fj2] [Fj2] Fujita, T., Classification of polarized manifolds of sectional genus two. In: Algebraic Geometry and Commutative Algebra, in Honor of Masayoshi Nagata, Kinokuniya, 1987, 73–98. Google Scholar

[Fk1] [Fk1] Fukuma, Y., A lower bound for the sectional genus of quasi-polarized surfaces. Geom.Dedicata 64 (1997), 229–251. Google Scholar

[Fk2] [Fk2] Fukuma, Y., A lower bound for sectional genus of quasi-polarized manifolds. J.Math. Soc. Japan 49 (1997), 339–362. Google Scholar

[Fk3] [Fk3] Fukuma, Y., On sectional genus of quasi-polarized 3-folds. Trans. Amer. Math. Soc., to appear. Google Scholar

[I] [I] Ionescu, P., Generalized adjunction and applications. Math. Proc. Cambridge Philos. Soc. 99 (1986), 457–472. Google Scholar

[Is] [Is] Ishihara, H., On polarized manifolds of sectional genus three. Kodai Math. J. 18 (1995), 328–343. Google Scholar

[KMM] [KMM] Kawamata, Y., Matsuda, K. and Matsuki, K., Introduction to the minimal model problem. Adv. Stud. Pure Math. 10 (1987), 283–360. Google Scholar

[LP] [LP] Lanteri, A. and Palleschi, M., About the adjunction process for polarized algebraic surfaces. J. Reine Angew. Math. 352 (1984), 15–23. Google Scholar

[So1] [So1] Sommese, A. J., Ample divisors on normal Gorenstein surfaces. Abh. Math. Sem. Univ. Hamburg 55 (1985), 151–170. Google Scholar

[So2] [So2] Sommese, A. J., On the adjunction theoretic structure of projective varieties. In: Proc. Complex Analysis and Algebraic Geometry Conf. 1985, Lecture Notes in Math., Springer, 1986, 175–213. Google Scholar

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