Skip Navigation

International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm025, 10 pages, doi:10.1093/imrn/rnm025 published on May 24, 2007
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Kumar, M. N.
Right arrow Articles by Ravindra, G. V.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Copyright © The Author 2007. Published by Oxford University Press.

Arithmetically Cohen-Macaulay Bundles on Three Dimensisonal Hypersurfaces

Mohan N. Kumar1, A. P. Rao2, and G. V. Ravindra3

1 Department of Mathematics, Washington University in St. Louis, St, Louis, Missouri, 63130
2 Department of Mathematics, University of Missouri-St. Louis, St. Louis Missouri, 63121
3 Department of Mathematics, India Institute of Science, Bangalore-560012, India

Correspondence: Correspondence to be sent to: A. P. Rao, Department of Mathematics, University of Missour-St. Louis, St Louis, Missouri, 63121. e-mail: rao{at}math.umsl.edu

We prove that any rank two arithmetically Cohen-Macaulay vector bundle on a general hypersurface of degree at least six in P4 must be split

Communicated by Enrico Arbarello



References

  1. Beauville A. Determinantal hypersurfaces. Michigan Mathematical Journal (2000) 48:39–64.[CrossRef]
  2. Buchweitz R.-O., Greuel G.-M., Schreyer F.-O. Cohen-Macaulay modules on hypersurface singularities. II. Inventiones Mathematicae (1987) 88(1):165–182.[CrossRef][Web of Science]
  3. Chiantini L., Madonna C. A splitting criterion for rank 2 bundles on a general sextic threefold. International Journal of Mathematics (2004) 15(4):341–359.[CrossRef][Web of Science]
  4. Eagon J., Northcott D. G. Ideals defined by matrices and a certain complex associated with them. Proceedings of the Royal Society A (1962) 269:188–204.[Abstract/Free Full Text]
  5. Horrocks G. Vector bundles on the punctured spectrum of a local ring. Proceedings of the London Mathematical Society (1964) 14(3):689–713.[CrossRef]
  6. Kleppe H. Deformation of schemes defined by vanishing of Pfaffians. Journal of Algebra (1978) 53(1):84–92.[CrossRef][Web of Science]
  7. Mohan Kumar N., Rao A. P., Ravindra G. V. Arithmetically Cohen-Macaulay vector bundles on hypersurfaces. Commentarii Mathematici Helvetici. (forthcoming).
  8. Mohan Kumar N., Rao A. P., Ravindra G. V. Four-by-Four Pfaffians. Rendiconti del Seminario Matematico Università e Politecnico di Torino (2006) 64(4):471–477.
  9. Northcott D. G. Multilinear Algebra (1984) Cambridge: Cambridge University Press. x+198.
  10. Okonek C. Notes on varieties of codimension 3 in Formula . Manuscripta Mathematica (1994) 84(3-4):421–442.[CrossRef][Web of Science]

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Kumar, M. N.
Right arrow Articles by Ravindra, G. V.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?