Lectures on vector bundles

Bibliographic Information

Lectures on vector bundles

J. Le Potier ; translated by A. Maciocia

(Cambridge studies in advanced mathematics, 54)

Cambridge University Press, 1997

Available at  / 69 libraries

Search this Book/Journal

Note

"Transferred to digital printing 2004"--T.p. verso of 2004 printing

Includes bibliographical references (p. 245-248) and index

Description and Table of Contents

Description

This work consists of two courses on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The construction and elementary properties of the moduli spaces of stable bundles are also discussed. In particular, Hilbert-Grothendieck schemes of vector bundles are constructed, and Mumford's geometric invariant theory is succinctly treated. The second part centres on the structure of the moduli space of semi-stable sheaves on the projective plane. Existence conditions for sheaves of given rank and Chern Class and construction ideas are sketched in the general context of projective algebraic surfaces. Professor Le Potier has provided a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Table of Contents

  • Part I. Vector Bundles On Algebraic Curves: 1. Generalities
  • 2. The Riemann-Roch formula
  • 3. Topological
  • 4. The Hilbert scheme
  • 5. Semi-stability
  • 6. Invariant geometry
  • 7. The construction of M(r,d)
  • 8. Study of M(r,d)
  • Part II. Moduli Spaces Of Semi-Stable Sheaves On The Projective Plane
  • 9. Introduction
  • 10. Operations on semi-stable sheaves
  • 11. Restriction to curves
  • 12. Bogomolov's theorem
  • 13. Bounded families
  • 14. The construction of the moduli space
  • 15. Differential study of the Shatz stratification
  • 16. The conditions for existence
  • 17. The irreducibility
  • 18. The Picard group
  • Bibliography.

by "Nielsen BookData"

Related Books: 1-1 of 1

Details

  • NCID
    BA29215895
  • ISBN
    • 0521481821
  • LCCN
    96013367
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Original Language Code
    fre
  • Place of Publication
    Cambridge [England]
  • Pages/Volumes
    viii, 251 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
Page Top