Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-10-06T12:30:33.650Z Has data issue: false hasContentIssue false
  • English
  • Français

Normal bundles in flag bundles

Published online by Cambridge University Press:  24 October 2008

Samuel A. Ilori
Samuel A. Ilori
Affiliation:
University of Ibadan, Nigeria
Get access Rights & Permissions [Opens in a new window]

Abstract

Let i: Y ↪ X be an inclusion map of non-singular irreducible algebraic quasi-projective varieties defined over an algebraically closed field. Let E be an algebraic vector bundle over X and H be a sub-bundle of the induced bundle, i*E. If j:F(H) ↪ F(E) is the corresponding inclusion map of (incomplete) flag bundles, then we derive the normal bundle N(F(H), F(E)) in terms of the bundles H and E, the tangent bundles of Y and X as well as the tautological bundles over F(H).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 3 , November 1981 , pp. 395 - 402
Copyright
Copyright © Cambridge Philosophical Society 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Borel, A.Linear algebraic groups (W. A. Benjamin, New York, 1969).Google Scholar
(2)Hirzebruch, F.Topological methods in algebraic geometry, 3rd ed. (Springer, Berlin, 1966).Google Scholar
(3)Lam, K. Y.A formula for the tangent bundle of flag manifolds and related manifolds. Trans. Amer. Math. Soc. 213 (1975), 305–314.CrossRefGoogle Scholar
(4)Lascu, A. T. and Scott, D. B.An algebraic correspondence with applications to projective bundles and blowing up Chern classes. Annali di Matematica Pura ed Applicata, (4) 102 (1975), 1–36.CrossRefGoogle Scholar
(5)Chevalley, Séminaire C.. Anneaux de Chow et applications (Secrétariat mathématique, 11 Rue Pierre Curie, Paris 5e, 1958).Google Scholar
(6)Porteous, I. R. Simple singularities of maps. Proc. Liverpool Singularities Symposium, vol. 1 (Springer Lecture Notes in Math., vol. 192).Google Scholar