Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On classification of polarized varieties with non-integral nef values


Author: Yicai Zhao
Journal: Proc. Amer. Math. Soc. 129 (2001), 1907-1913
MSC (2000): Primary 14Jxx
DOI: https://doi.org/10.1090/S0002-9939-00-05827-5
Published electronically: December 4, 2000
MathSciNet review: 1825896
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

Let $M$ be an $n$-dimensional normal projective variety with only Gorenstein, terminal, $\mathbb{Q}$-factorial singularities. Let $L$ be an ample line bundle on $M$. Let $\tau$ denote the nef value of $(M,L)$. The classification of $(M,L)$ via the nef value morphism is given for the situations when $\tau$satisfies $n-3<\tau<n-2$ or $n-4<\tau<n-3$.


References [Enhancements On Off] (What's this?)

  • [An] M. Andreatta, Contractions of Gorenstein polarized varieties with high nef value, Math. Ann. 300 (1994), 669-679. MR 96b:14007
  • [BS1] M. Beltrametti and J. A. Sommese, On the adjunction theoretic classification of polarized varieties, J. Reine. Angew. Math. 427 (1992), 157-192. MR 93d:14012
  • [BS2] M. Beltrametti and J. A. Sommese, A remark on the Kawamata rationality theorem, J. Math. Soc. Japan 45 (1993), 557-568. MR 94e:14006
  • [F1] T. Fujita, Remarks on quasi-polarized varieties, Nagoya Math. J. 115 (1989), 105-123. MR 90i:14045
  • [F2] T. Fujita, On Kodaira energy and adjoint reduction of polarized manifolds, Manuscr. Math. 75 (1992), 59-84. MR 93i:14032
  • [KMM] Y. Kawamata, K. Matsuda, K. Matsuki, Introduction to the Minimal Model Program, Advanced Studies in Pure Math. 10 (1987), 283-360. MR 89e:14015
  • [Ma] H. Maeda, Ramification divisors for branched coverings of $\mathbb{P}^n$, Math. Ann. 288 (1990), 195-199. MR 91i:14011
  • [Mo] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. Math. 116 (1982), 133-176. MR 84e:14032
  • [S] A. J. Sommese, On the adjunction theoretic structure of projective varieties, Lecture Notes Math. 1194 (1984), 175-213. MR 87m:14049

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14Jxx

Retrieve articles in all journals with MSC (2000): 14Jxx


Additional Information

Yicai Zhao
Affiliation: Department of Mathematics, Jinan University, Guangzhou 510632, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-00-05827-5
Keywords: Nef value morphism, ample line bundle, projective variety
Received by editor(s): September 14, 1998
Received by editor(s) in revised form: November 1, 1999
Published electronically: December 4, 2000
Communicated by: Ron Donagi
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society