Skip to main content Accessibility help
×
Home

Numerical Criteria for Very Ampleness of Divisors on Projective Bundles Over an Elliptic Curve

  • Alberto Alzati (a1), Marina Bertolini (a2) and Gian Mario Besana (a3)

Abstract

Let D be a divisor on a projectivized bundle over an elliptic curve. Numerical conditions for the very ampleness of D are proved. In some cases a complete numerical characterization is found.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Numerical Criteria for Very Ampleness of Divisors on Projective Bundles Over an Elliptic Curve
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Numerical Criteria for Very Ampleness of Divisors on Projective Bundles Over an Elliptic Curve
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Numerical Criteria for Very Ampleness of Divisors on Projective Bundles Over an Elliptic Curve
      Available formats
      ×

Copyright

References

Hide All
1. Atiyah, M. F., Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7(1957), 414452.
2. Beltrametti, M. C. and Sommese, A. J., The Adjunction Theory of Complex Projective Varieties, Exposition. Math. 16, cDe Gruyter, 1995.
3. Biancofiore, A. and Livorni, E. L., On the Genus of a Hyperplane Section of a Geometrically Ruled Surface, Ann. Mat. Pura Appl. 147(1987), 173185.
4. Butler, D. C., Normal generation of vector bundles over a curve, J. Differential Geom. (1) 39(1994), 134.
5. Griffiths, P. and Harris, J., Principles of Algebraic Geometry, John Wiley & Sons, 1978.
6. Gushel, N. P., Very ample divisors on projective bundles over an elliptic curve, Mat. Zametki (6) 47(1990), 1522.
7. Gushel, N. P., Very ample divisors on projective bundles over curves, St. Petersburg Math. J. (2) 4(1993), 297307.
8. Hartshorne, R., Ample vector bundles on curves, Nagoya Math. J. 43(1971), 4172.
9. Hartshorne, R., Algebraic Geometry, Graduate Texts in Math. 52, Springer Verlag, New York, Heidelberg, Berlin, 1977.
10. Miyaoka, Y., The Chern class and Kodaira dimension of a minimal variety. In: Algebraic Geometry, Sendai 1985, Adv. Stud. Pure Math. 10, Amer. Math. Soc., 1987, 449476.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Numerical Criteria for Very Ampleness of Divisors on Projective Bundles Over an Elliptic Curve

  • Alberto Alzati (a1), Marina Bertolini (a2) and Gian Mario Besana (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed