Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-13T18:01:12.133Z Has data issue: false hasContentIssue false
  • English
  • Français

P-Ample Bundles and Their Chern Classes

Published online by Cambridge University Press:  22 January 2016

David Gieseker
David Gieseker*
Affiliation:
University of California Santa Cruz, California
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In [9], Hartshorne extended the concept of ampleness from line bundles to vector bundles. At that time, he conjectured that the appropriate Chern classes of an ample vector bundle were positive, and it was hoped that there would be some criterion for ampleness of vector bundles similar to Nakai’s criterion for line bundles. In the same paper, Hartshorne also introduced the notion of p-ample when the ground field had characteristic p, proved that a p-ample bundle was ample and asked if the converse were true.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 43 , September 1971, pp. 91 - 116
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Atiyah, M.F., Vector Bundles Over an Elliptic Curve, Proc. Lond. Math. Soc, 3, VII (1957), 414–452.Google Scholar
[2] Barton, C., Tensor Products of Ample Bundles in Characteristic p (to appear).Google Scholar
[3] Barton, C., Contributions to the Theory of Ample Vector Bundles, Thesis, Columbia University, 1968.Google Scholar
[4] Bloch, S. and Gieseker, D., The Positivity of the Chern Classes of an Ample Vector Bundle, Invent, math. 12 (1971), 112–117.CrossRefGoogle Scholar
[5] Griffiths, P.A., The Extension Problem in Complex Analysis II. Embeddings with Positive Normal Bundle, Amer. J. Math. 88 (2) (1965), 366–446.CrossRefGoogle Scholar
[6] Griffiths, P.A., Hermitian differential geometry, Chern classes, and positive vector bundles, in Global Analysis, edited by Spencer, D.C. and Iyanaga, S., Princeton Mathematical Series, No. 29, Tokyo, 1969.Google Scholar
[7] Grothendieck, A., La Théorie des Classes de Chern, Bull. Soc. Math. France 86 (1958), 137–154.Google Scholar
[8] Grothendieck, A. and Dieudonné, J., Éléments de Géométrie Algébrique, Publ. Math. IHES 1960 ff.Google Scholar
[9] Hartshorne, R., Ample Vector Bundles, Publ. Math. IHES 29 (1966), 63–94.CrossRefGoogle Scholar
[10] Hartshorne, R., Cohomological Dimension of Algebraic Varieties, Ann. of Math. 88 (3), 1968, 403–450.Google Scholar
[11] Hartshorne, R., Ample Vector Bundles on Curves, Nagoya Math. J. Vol. 43 (this volume).Google Scholar
[12] Kleiman, S.L., Towards a Numerical Theory of Ampleness, Ann. of Math. 84 (2) (1966), 291–344.Google Scholar
[13] Kleiman, S.L., Ample Vector Bundles on Surfaces, Proc. Amer. Math. Soc. 21, No. 3, June 1969, 673–676.CrossRefGoogle Scholar