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ON A CONJECTURE OF BELTRAMETTI–SOMMESE FOR POLARIZED 3-FOLDS

YOSHIAKI FUKUMA

Department of Mathematics, Faculty of Science, Kochi University, Akebono-cho, Kochi 780-8520, Japan

https://doi.org/10.1142/S0129167X06003709Cited by:13 (Source: Crossref)

Abstract

Let (X, L) be a polarized manifold of dimension 3. In this paper, we consider a lower bound for h⁰(K_X + 2L). We prove that h⁰(K_X + 2L) > 0 if K_X + 2L is nef, which is a conjecture of Beltrametti–Sommese for polarized 3-folds. Moreover we classify polarized 3-folds (X, L) with h⁰(K_X + 2L) = 1 under the assumption that K_X + 2L is nef.

Keywords:

AMSC: Primary 14C20, Secondary 14J30, Secondary 14J35, Secondary 14J40

References

M. C. Beltrametti and A. J. Sommese , The Adjunction Theory of Complex Projective Varieties , de Gruyter Expositions in Mathematics 16 ( Walter de Gruyter , Berlin, New York , 1995 ) . Crossref, Google Scholar
M. C. Beltrametti and A. J. Sommese, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22, 1 (1995), MR 96e:14005. Google Scholar
J. A. Chen and C. D. Hacon, Algebraic Geometry in East Asia (Kyoto 2001) (World Scientific Publishing, River Edge, NJ, 2002) pp. 143–153. Link, Google Scholar
T. Fujita, Classification of polarized manifolds of sectional genus two, Proceedings of "Algebraic Geometry and Commutative Algebra" in Honor of Masayoshi Nagata (1987) pp. 73–98. Google Scholar
T. Fujita, J. Math. Kyoto Univ. 29, 1 (1989). Crossref, Web of Science, Google Scholar
T. Fujita , Classification Theories of Polarized Varieties , London Mathematical Society Lecture Note Series 155 ( Cambridge University Press , 1990 ) . Crossref, Google Scholar
Y. Fukuma, Geom. Dedicata 64, 229 (1997). Crossref, Web of Science, Google Scholar
Y. Fukuma,, Ark. Mat. 35, 299 (1997). Crossref, Web of Science, Google Scholar
Y. Fukuma, Geom. Dedicata 69, 189 (1998). Crossref, Web of Science, Google Scholar
Y. Fukuma, Canad. Math. Bull. 41, 267 (1998). Crossref, Web of Science, Google Scholar
Y. Fukuma, Trans. Amer. Math. Soc. 351, 363 (1999). Crossref, Web of Science, Google Scholar
Y. Fukuma, Math. Z. 234, 573 (2000). Crossref, Web of Science, Google Scholar
Y. Fukuma, Commun Algebra 32, 1069 (2004). Crossref, Web of Science, Google Scholar
Y. Fukuma, Manuscripta Math. 113, 211 (2004). Crossref, Web of Science, Google Scholar
Y. Fukuma, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 25, 55 (2004). Web of Science, Google Scholar
Y. Fukuma, Adv. Geom. 5, 431 (2005). Crossref, Web of Science, Google Scholar
Y. Fukuma, Math. Z. 250, 573 (2005). Crossref, Web of Science, Google Scholar
F. Hirzebruch , Topological Methods in Algebraic Geometry 131 ( Springer-Verlag , 1966 ) . Crossref, Google Scholar
P. Ionescu, Math. Proc. Cambridge Phil. Soc. 99, 457 (1986). Crossref, Web of Science, Google Scholar
H. Ishihara, Kodai Math. J. 18, 328 (1995). Crossref, Google Scholar
R. Miyaoka and M. Kotani (eds.) , Mathematics in the 21 Century, Unscaled Peaks of Geometry ( Nihon Hyōronsha , Japan , 2004 ) . Google Scholar
A. J. Sommese, On the adjunction theoretic structure of projective varieties, Proc. Complex Anal. Algebraic Geom. Conf., Lecture Notes in Mathematics 1194 (Springer-Verlag, New York, 1985) pp. 175–213. Google Scholar