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)

 
 

 

Ample and spanned vector bundles of top Chern number two on smooth projective varieties


Author: Atsushi Noma
Journal: Proc. Amer. Math. Soc. 126 (1998), 35-43
MSC (1991): Primary 14F05, 14J60; Secondary 14C05
DOI: https://doi.org/10.1090/S0002-9939-98-04464-5
MathSciNet review: 1459141
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to classify ample and spanned vector bundles of top Chern number two on smooth projective varieties of arbitrary dimension defined over an algebraically closed field of characteristic zero.


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

  • 1. M. F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414-452. MR 24:A1274
  • 2. E. Ballico, Rank-$2$ vector bundles with many sections and low $c_{2}$ on a surface, Geom. Dedicata 29 (1989), 109-124. MR 90e:14014
  • 3. E. Ballico and A. Lanteri, An indecomposable rank-$2$ vector bundle the complete linear system of whose determinant consists of hyperelliptic curves, Boll. Un. Mat. Ital. (7) 3-A (1989), 225-230. MR 90j:14022
  • 4. M. C. Beltrametti and A. J. Sommese, The adjunction theory of complex projective varieties, de Gruyter Exp. Math. 16, de Gruyter, Berlin, 1995. MR 96f:14004
  • 5. T. Fujita, Classification theories of polarized varieties, London Math. Soc. Lecture Note Ser. Vol. 155, 1990. MR 93e:14009
  • 6. T. Fujita, On adjoint bundles of ample vector bundles, Complex Algebraic Varieties, Proceedings, Bayreuth 1990 (K. Hulek et al., eds.), Lecture Notes in Math., vol. 1507, Springer-Verlag, 1992, pp. 105-112. MR 93j:14052
  • 7. D. Gieseker, p-ample bundles and their Chern classes, Nagoya Math. J. 43 (1971), 91-116. MR 45:5139
  • 8. P. Griffiths and J. Harris, Residues and zero-cycles on algebraic varieties, Ann. of Math. 108 (1978), 461-505. MR 80d:14006
  • 9. Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. MR 86c:14013b
  • 10. A. Lanteri and F. Russo, A footnote to a paper by Noma, Rend. Mat. Acc. Lincei (9) 4 (1993), 131-132. MR 95a:14045
  • 11. A. Lanteri and A. J. Sommese, A vector bundle characterization of $\mathbb{P}^{n}$, Abh. Math. Sem. Univ. Hamburg 58 (1988), 89-94. MR 91e:14054
  • 12. S. Mukai and F. Sakai, Maximal subbundles of vector bundles on a curve, Manuscripta Math. 52 (1985), 251-256. MR 86k:14013
  • 13. A. Noma, Classification of rank-two ample and spanned vector bundles on surfaces whose zero loci consist of general points, Transactions Amer. Math. Soc. 342 (1994), 867-894. MR 89f:14040
  • 14. A. Noma, Ample and spanned vector bundles of $c_{2} =2$ on normal Gorenstein surfaces, preprint.
  • 15. A. Wi\'{s}niewski, Length of extremal rays and generalized adjunction, Math. Z. 200 (1989), 409-427. MR 91e:14032
  • 16. Q. Zhang, Ample vector bundles on singular varieties, Math. Z. 220 (1995), 59-64. MR 96i:14034
  • 17. Q. Zhang, Ample vector bundles on singular varieties II, Math. Ann. 307 (1997), 505-509. CMP 97:09

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14F05, 14J60, 14C05

Retrieve articles in all journals with MSC (1991): 14F05, 14J60, 14C05


Additional Information

Atsushi Noma
Affiliation: Department of Mathematics, Faculty of Education, Yokohama National University, 156 Tokiwadai, Hodogaya, Yokohama 240, Japan
Email: noma@ms.ed.ynu.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-98-04464-5
Keywords: ample vector bundle, spanned vector bundle, zero cycle, adjunction map
Received by editor(s): April 29, 1996
Communicated by: Ron Donagi
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society